Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Find the wrong term in the following number series.
24, 26, 36, 62, 112, 196, 316
36
26
112
196
316
Correct answer
196
Why this answer is correct
Given:
24, 26, 36, 62, 112, 196, 316
Calculation:
⇒ 24 + 2 (12 +1) = 26
⇒ 26 + 10 (32 +1) = 36
⇒ 36 + 26 (52 +1) = 62
⇒ 62 + 50 (72 +1) = 112
⇒ 112 + 82 (92 +1) = 194
⇒ 194 + 122 (112 +1) = 316
∴ The wrong term is 196.
Find the wrong term in the following number series.
155, 298, 493, 748,1069, 1470
155
493
1069
748
1470
Correct answer
1069
Why this answer is correct
Given:
155, 298, 493, 748,1069, 1470
Calculation:
⇒ 155 + (122 - 1) = 298
⇒ 298 + (142 - 1) = 493
⇒ 493 + (162 - 1) = 748
⇒ 748 + (182 - 1) = 1071
⇒ 1071 + (202 - 1) = 1470
∴ The wrong term is 1069.
In each of the following number series, the wrong number is given, find out that number.
25, 200, 45, 320, 64, 512
200
45
64
512
320
Correct answer
45
Why this answer is correct
Given:
25, 200, 45, 320, 64, 512
Calculation:
⇒ 25 × 8 = 200
⇒ 200 ÷ 5 = 40
⇒ 40 × 8 = 320
⇒ 320 ÷ 5 = 64
⇒ 64 × 8 = 512
∴ The wrong term is 45.
In each of the following number series, the wrong number is given, find out that number.
119, 138, 195, 290, 432, 594
138
432
594
290
195
Correct answer
432
Why this answer is correct
Given:
119, 138, 195, 290, 432, 594
Calculation:
⇒ 119 + 19 × 1 = 138
⇒ 138 + 19 × 3 = 195
⇒ 195 + 19 × 5 = 290
⇒ 290 + 19 × 7 = 423
⇒ 423 + 19 × 9 = 594.
∴ The wrong term is 432.
Two typists of varying skill can do a job in 18 minutes if they work together. If the first typist alone typed for 9 minutes and then the second typist alone typed for 18 minutes, they would be left with 1/3rd of the entire work. How many minutes would it take for the faster typist to complete the typing job working alone?
37 minutes
27 minutes
47 minutes
17 minutes
None of these
Correct answer
27 minutes
Why this answer is correct
Shortcut Trick
Let efficiencies of typists be x and y. Total work = 18(x + y).
Work done: 9x + 18y = 2/3 of 18(x + y) ⇒ 9x + 18y = 12x + 12y.
⇒ 6y = 3x ⇒ x = 2y. Ratio of efficiencies x : y = 2 : 1.
Total Work = 18 × (2 + 1) = 54 units.
Time for faster typist (x) = 54 ÷ 2 = 27 minutes.
∴ The correct answer is 27 min.
Alternate Method
| Person | Time (min) | Total Work (W) | Efficiency |
|---|---|---|---|
| Typist 1 + 2 | 18 | W | W/18 |
Given: First typist works for 9 min, Second for 18 min, remaining work is 1/3.
⇒ Work completed = 1 − 1/3 = 2/3 of total work.
⇒ Let efficiency of first typist be a and second be b.
⇒ Total Work = 18(a + b)
⇒ 9a + 18b = (2/3) × 18(a + b)
⇒ 9a + 18b = 12a + 12b
⇒ 18b − 12b = 12a − 9a
⇒ 6b = 3a ⇒ a = 2b (First typist is faster)
⇒ Total Work = 18(2b + b) = 18 × 3b = 54b
⇒ Time for faster typist = 54b ÷ 2b = 27 minutes.
∴ The correct answer is 27 min.
Additional Information
Efficiency and Time Relation
Efficiency is inversely proportional to time taken. If the ratio of efficiencies is a : b, then the ratio of time taken is b : a.
Combined Work Formula
If two people with efficiencies E1 and E2 work together for T days, the Total Work = T × (E1 + E2).
In a class of N students, 59% students passed in History, 72% students passed in Political Science and 35% students passed in both subjects. If 666 students passed in only Political Science, then, what is the value of N?
1600
1800
2000
2100
None of these
Correct answer
1800
Why this answer is correct
Shortcut Trick
Students passed in only Political Science = Total passed in Pol. Science − passed in Both
Percentage in only Pol. Science = 72% − 35% = 37%
Given, 37% of N = 666
N = 666 ÷ 37 × 100 = 18 × 100 = 1800
∴ The correct answer is 1800 students.
Alternate Method
Given:
Passed in History H = 59%
Passed in Political Science P = 72%
Passed in Both (H ∩ P) = 35%
Number of students passed in only Political Science = 666
Calculations:
⇒ Percentage of students passed in only Political Science = P − (H ∩ P)
⇒ Percentage = 72% − 35% = 37%
⇒ According to the question, 37% of N = 666
⇒ (37/100) × N = 666
⇒ N = (666 × 100) ÷ 37
⇒ N = 18 × 100
⇒ N = 1800
∴ The correct answer is 1800 students.
Additional Information
Venn Diagram Principle
For two sets A and B, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). This represents students who passed in at least one subject.
Only One Subject Calculation
To find only A, subtract the intersection from total A: n(only A) = n(A) − n(A ∩ B).
Failed in Both Subjects
Percentage failed in both subjects = 100% − [Percentage passed in at least one subject].
Directions: The given table below show the number of students (males + females) participated exam and percentage of students out of total failed and number of males failed in exam in five different colleges.
| Colleges | Number of students (Male + female)participated in exam | Ratio between number of males to females participated in exam | Percentage of students (male + female) failed out of total participated | Number of males failed out of total males participated |
|---|---|---|---|---|
| A | 1100 | 7: 4 | 30% | 210 |
| B | 900 | 2: 1 | 40% | 240 |
| C | 1400 | 4: 3 | 50% | 500 |
| D | 1400 | 17: 11 | 45% | 255 |
| E | 1600 | 9: 7 | 60% | 450 |
Number of students participated = Number of students failed + Number of students passed
Number of males who passed exam in college A is 3/7 are scored in distinction and 3/5 of the females who passed exam in college A are scored in distinction, then find the total number of students in college A passed in distinction.
374
322
378
344
369
Correct answer
378
Why this answer is correct
General Solution:
College A:
Total number of students (Male + Female) participated in exam = 1100
Number of males participated in exam = 1100/11 × 7 = 700
Number of females participated in exam = (1100 - 700) = 400
Percentage of students failed in exam = 1100 × (30/100) = 330
Number females failed in exam = 330 - 210 = 120
Number of males passed in exam = 700 - 210 = 490
Number of females passed in exam = 400 - 120 = 280
College B:
Total number of students (Male + Female) participated in exam = 900
Number of males participated in exam = 900/3 × 2 = 600
Number of females participated in exam = (900 - 600) = 300
Percentage of students failed in exam = 900 × (40/100) = 360
Number females failed in exam = 360 - 240 = 120
Number of males passed in exam = 600 - 240 = 360
Number of females passed in exam = 300 - 120 = 180
College C:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/3 × 4 = 800
Number of females participated in exam = (1400 - 800) = 600
Percentage of students failed in exam = 1140 × (50/100) = 700
Number females failed in exam = 700 - 500 = 200
Number of males passed in exam = 800 - 500 = 300
Number of females passed in exam = 600 - 200 = 400
College D:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/28 × 17 = 850
Number of females participated in exam = (1400 - 850) = 550
Percentage of students failed in exam = 1400 × (45/100) = 630
Number females failed in exam = 630 - 255 = 375
Number of males passed in exam = 850 - 255 = 595
Number of females passed in exam = 550 - 375 = 175
College E:
Total number of students (Male + Female) participated in exam = 1600
Number of males participated in exam = 1600/16 × 9 = 900
Number of females participated in exam = (1600 - 900) = 700
Percentage of students failed in exam = 1600 × (60/100) = 960
Number females failed in exam = 960 - 450 = 510
Number of males passed in exam = 900 - 450 = 450
Number of females passed in exam = 700 - 510 = 190
| College | Number of males passed in exam | Number of female passed in exam | Number of males failed in exam | Number of female failed in exam |
|---|---|---|---|---|
| A | 490 | 280 | 210 | 120 |
| B | 360 | 180 | 240 | 120 |
| C | 300 | 400 | 500 | 200 |
| D | 595 | 175 | 255 | 375 |
| E | 450 | 190 | 450 | 510 |
Solution:
Number of males who passed in college A = 490
Number of male who passed in college A passed in distinction = 490 × (3/7) = 210
Number of females passed in college A = 280
Number of females who passed in college A in distinction = (280 × 3/5) = 168
Required total = (210 + 168) = 378
Directions: The given table below show the number of students (males + females) participated exam and percentage of students out of total failed and number of males failed in exam in five different colleges.
| Colleges | Number of students (Male + female)participated in exam | Ratio between number of males to females participated in exam | Percentage of students (male + female) failed out of total participated | Number of males failed out of total males participated |
|---|---|---|---|---|
| A | 1100 | 7: 4 | 30% | 210 |
| B | 900 | 2: 1 | 40% | 240 |
| C | 1400 | 4: 3 | 50% | 500 |
| D | 1400 | 17: 11 | 45% | 255 |
| E | 1600 | 9: 7 | 60% | 450 |
Number of students participated = Number of students failed + Number of students passed
If the number of males and females failed in college B respectively are increased by 30% and 40% respectively. Find the total number of students who failed in college B is how much more or less than the number of students passed in the same college.
50
20
40
60
80
Correct answer
60
Why this answer is correct
General Solution:
College A:
Total number of students (Male + Female) participated in exam = 1100
Number of males participated in exam = 1100/11 × 7 = 700
Number of females participated in exam = (1100 - 700) = 400
Percentage of students failed in exam = 1100 × (30/100) = 330
Number females failed in exam = 330 - 210 = 120
Number of males passed in exam = 700 - 210 = 490
Number of females passed in exam = 400 - 120 = 280
College B:
Total number of students (Male + Female) participated in exam = 900
Number of males participated in exam = 900/3 × 2 = 600
Number of females participated in exam = (900 - 600) = 300
Percentage of students failed in exam = 900 × (40/100) = 360
Number females failed in exam = 360 - 240 = 120
Number of males passed in exam = 600 - 240 = 360
Number of females passed in exam = 300 - 120 = 180
College C:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/3 × 4 = 800
Number of females participated in exam = (1400 - 800) = 600
Percentage of students failed in exam = 1140 × (50/100) = 700
Number females failed in exam = 700 - 500 = 200
Number of males passed in exam = 800 - 500 = 300
Number of females passed in exam = 600 - 200 = 400
College D:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/28 × 17 = 850
Number of females participated in exam = (1400 - 850) = 550
Percentage of students failed in exam = 1400 × (45/100) = 630
Number females failed in exam = 630 - 255 = 375
Number of males passed in exam = 850 - 255 = 595
Number of females passed in exam = 550 - 375 = 175
College E:
Total number of students (Male + Female) participated in exam = 1600
Number of males participated in exam = 1600/16 × 9 = 900
Number of females participated in exam = (1600 - 900) = 700
Percentage of students failed in exam = 1600 × (60/100) = 960
Number females failed in exam = 960 - 450 = 510
Number of males passed in exam = 900 - 450 = 450
Number of females passed in exam = 700 - 510 = 190
| College | Number of males passed in exam | Number of female passed in exam | Number of males failed in exam | Number of female failed in exam |
|---|---|---|---|---|
| A | 490 | 280 | 210 | 120 |
| B | 360 | 180 | 240 | 120 |
| C | 300 | 400 | 500 | 200 |
| D | 595 | 175 | 255 | 375 |
| E | 450 | 190 | 450 | 510 |
Solution:
Number of males failed in college B = 240
Number of females failed in college B = 120
Number of males failed in college B increased by 30% = 240 × (130/100) = 312
Number of females failed in college B increased by 40% = 120 × (140/100) = 168
Total students passed in the college B = 540
Required difference = 540 - 480 = 60
Directions: The given table below show the number of students (males + females) participated exam and percentage of students out of total failed and number of males failed in exam in five different colleges.
| Colleges | Number of students (Male + female)participated in exam | Ratio between number of males to females participated in exam | Percentage of students (male + female) failed out of total participated | Number of males failed out of total males participated |
|---|---|---|---|---|
| A | 1100 | 7: 4 | 30% | 210 |
| B | 900 | 2: 1 | 40% | 240 |
| C | 1400 | 4: 3 | 50% | 500 |
| D | 1400 | 17: 11 | 45% | 255 |
| E | 1600 | 9: 7 | 60% | 450 |
Number of students participated = Number of students failed + Number of students passed
3/5 of the number of males passed in college D and 4/5 of the number females passed in college D are approximately what percentage of the total number of students failed in the same college.
80%
72%
79%
65%
75%
Correct answer
79%
Why this answer is correct
General Solution:
College A:
Total number of students (Male + Female) participated in exam = 1100
Number of males participated in exam = 1100/11 × 7 = 700
Number of females participated in exam = (1100 - 700) = 400
Percentage of students failed in exam = 1100 × (30/100) = 330
Number females failed in exam = 330 - 210 = 120
Number of males passed in exam = 700 - 210 = 490
Number of females passed in exam = 400 - 120 = 280
College B:
Total number of students (Male + Female) participated in exam = 900
Number of males participated in exam = 900/3 × 2 = 600
Number of females participated in exam = (900 - 600) = 300
Percentage of students failed in exam = 900 × (40/100) = 360
Number females failed in exam = 360 - 240 = 120
Number of males passed in exam = 600 - 240 = 360
Number of females passed in exam = 300 - 120 = 180
College C:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/3 × 4 = 800
Number of females participated in exam = (1400 - 800) = 600
Percentage of students failed in exam = 1140 × (50/100) = 700
Number females failed in exam = 700 - 500 = 200
Number of males passed in exam = 800 - 500 = 300
Number of females passed in exam = 600 - 200 = 400
College D:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/28 × 17 = 850
Number of females participated in exam = (1400 - 850) = 550
Percentage of students failed in exam = 1400 × (45/100) = 630
Number females failed in exam = 630 - 255 = 375
Number of males passed in exam = 850 - 255 = 595
Number of females passed in exam = 550 - 375 = 175
College E:
Total number of students (Male + Female) participated in exam = 1600
Number of males participated in exam = 1600/16 × 9 = 900
Number of females participated in exam = (1600 - 900) = 700
Percentage of students failed in exam = 1600 × (60/100) = 960
Number females failed in exam = 960 - 450 = 510
Number of males passed in exam = 900 - 450 = 450
Number of females passed in exam = 700 - 510 = 190
| College | Number of males passed in exam | Number of female passed in exam | Number of males failed in exam | Number of female failed in exam |
|---|---|---|---|---|
| A | 490 | 280 | 210 | 120 |
| B | 360 | 180 | 240 | 120 |
| C | 300 | 400 | 500 | 200 |
| D | 595 | 175 | 255 | 375 |
| E | 450 | 190 | 450 | 510 |
Solution:
Number of male students passed in college D = 595
Number of female students passed in college D = 175
3/5 of number of males passed in college D = 595 × 3/5 = 357
4/5 of number of females passed in college D = 175 × (4/5) = 140
Total students failed in college D = (255 + 375) = 630
Required percentage = (357 + 140)/630 × 100= 78.89%~ 79%
Directions: The given table below show the number of students (males + females) participated exam and percentage of students out of total failed and number of males failed in exam in five different colleges.
| Colleges | Number of students (Male + female)participated in exam | Ratio between number of males to females participated in exam | Percentage of students (male + female) failed out of total participated | Number of males failed out of total males participated |
|---|---|---|---|---|
| A | 1100 | 7: 4 | 30% | 210 |
| B | 900 | 2: 1 | 40% | 240 |
| C | 1400 | 4: 3 | 50% | 500 |
| D | 1400 | 17: 11 | 45% | 255 |
| E | 1600 | 9: 7 | 60% | 450 |
Number of students participated = Number of students failed + Number of students passed
Find the ratio between the number of males passed in college C and E to the number of females passed in the college C and E.
87: 90
75: 59
67: 61
75: 71
83: 77
Correct answer
75: 59
Why this answer is correct
General Solution:
College A:
Total number of students (Male + Female) participated in exam = 1100
Number of males participated in exam = 1100/11 × 7 = 700
Number of females participated in exam = (1100 - 700) = 400
Percentage of students failed in exam = 1100 × (30/100) = 330
Number females failed in exam = 330 - 210 = 120
Number of males passed in exam = 700 - 210 = 490
Number of females passed in exam = 400 - 120 = 280
College B:
Total number of students (Male + Female) participated in exam = 900
Number of males participated in exam = 900/3 × 2 = 600
Number of females participated in exam = (900 - 600) = 300
Percentage of students failed in exam = 900 × (40/100) = 360
Number females failed in exam = 360 - 240 = 120
Number of males passed in exam = 600 - 240 = 360
Number of females passed in exam = 300 - 120 = 180
College C:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/3 × 4 = 800
Number of females participated in exam = (1400 - 800) = 600
Percentage of students failed in exam = 1140 × (50/100) = 700
Number females failed in exam = 700 - 500 = 200
Number of males passed in exam = 800 - 500 = 300
Number of females passed in exam = 600 - 200 = 400
College D:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/28 × 17 = 850
Number of females participated in exam = (1400 - 850) = 550
Percentage of students failed in exam = 1400 × (45/100) = 630
Number females failed in exam = 630 - 255 = 375
Number of males passed in exam = 850 - 255 = 595
Number of females passed in exam = 550 - 375 = 175
College E:
Total number of students (Male + Female) participated in exam = 1600
Number of males participated in exam = 1600/16 × 9 = 900
Number of females participated in exam = (1600 - 900) = 700
Percentage of students failed in exam = 1600 × (60/100) = 960
Number females failed in exam = 960 - 450 = 510
Number of males passed in exam = 900 - 450 = 450
Number of females passed in exam = 700 - 510 = 190
| College | Number of males passed in exam | Number of female passed in exam | Number of males failed in exam | Number of female failed in exam |
|---|---|---|---|---|
| A | 490 | 280 | 210 | 120 |
| B | 360 | 180 | 240 | 120 |
| C | 300 | 400 | 500 | 200 |
| D | 595 | 175 | 255 | 375 |
| E | 450 | 190 | 450 | 510 |
Solution:
Number of males passed in college C = 300
Number of males passed in college E = 450
Number of females passed in college C = 400
Number of females passed in college E = 190
Required ratio = (450 + 300): (400 + 190) = 750: 590 = 75: 59
Directions: The given table below show the number of students (males + females) participated exam and percentage of students out of total failed and number of males failed in exam in five different colleges.
| Colleges | Number of students (Male + female)participated in exam | Ratio between number of males to females participated in exam | Percentage of students (male + female) failed out of total participated | Number of males failed out of total males participated |
|---|---|---|---|---|
| A | 1100 | 7: 4 | 30% | 210 |
| B | 900 | 2: 1 | 40% | 240 |
| C | 1400 | 4: 3 | 50% | 500 |
| D | 1400 | 17: 11 | 45% | 255 |
| E | 1600 | 9: 7 | 60% | 450 |
Number of students participated = Number of students failed + Number of students passed
Find the difference between the average number of males who failed in all the colleges and the average number of females who failed in all the colleges.
79
73
66
72
74
Correct answer
66
Why this answer is correct
General Solution:
College A:
Total number of students (Male + Female) participated in exam = 1100
Number of males participated in exam = 1100/11 × 7 = 700
Number of females participated in exam = (1100 - 700) = 400
Percentage of students failed in exam = 1100 × (30/100) = 330
Number females failed in exam = 330 - 210 = 120
Number of males passed in exam = 700 - 210 = 490
Number of females passed in exam = 400 - 120 = 280
College B:
Total number of students (Male + Female) participated in exam = 900
Number of males participated in exam = 900/3 × 2 = 600
Number of females participated in exam = (900 - 600) = 300
Percentage of students failed in exam = 900 × (40/100) = 360
Number females failed in exam = 360 - 240 = 120
Number of males passed in exam = 600 - 240 = 360
Number of females passed in exam = 300 - 120 = 180
College C:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/3 × 4 = 800
Number of females participated in exam = (1400 - 800) = 600
Percentage of students failed in exam = 1140 × (50/100) = 700
Number females failed in exam = 700 - 500 = 200
Number of males passed in exam = 800 - 500 = 300
Number of females passed in exam = 600 - 200 = 400
College D:
Total number of students (Male + Female) participated in exam = 1400
Number of males participated in exam = 1400/28 × 17 = 850
Number of females participated in exam = (1400 - 850) = 550
Percentage of students failed in exam = 1400 × (45/100) = 630
Number females failed in exam = 630 - 255 = 375
Number of males passed in exam = 850 - 255 = 595
Number of females passed in exam = 550 - 375 = 175
College E:
Total number of students (Male + Female) participated in exam = 1600
Number of males participated in exam = 1600/16 × 9 = 900
Number of females participated in exam = (1600 - 900) = 700
Percentage of students failed in exam = 1600 × (60/100) = 960
Number females failed in exam = 960 - 450 = 510
Number of males passed in exam = 900 - 450 = 450
Number of females passed in exam = 700 - 510 = 190
| College | Number of males passed in exam | Number of female passed in exam | Number of males failed in exam | Number of female failed in exam |
|---|---|---|---|---|
| A | 490 | 280 | 210 | 120 |
| B | 360 | 180 | 240 | 120 |
| C | 300 | 400 | 500 | 200 |
| D | 595 | 175 | 255 | 375 |
| E | 450 | 190 | 450 | 510 |
Solution:
Number of males who failed in all the college = (210 + 240 + 500 + 255 + 450)/5 = 331
Number of females who failed in all the college = (120 + 120 + 200 + 375 + 510)/5 = 265
Required difference = (331 - 265) = 66
The average height of A, B, C and D is 40 inches. A new person E is also included in the group, then the average height of the group is increased by 1 inch. Again a new person F replaces A then the new average of five people becomes 42. Find the average height of B, C, D, F.
42.75
41.75
42.25
43.25
41.25
Correct answer
41.25
Why this answer is correct
Shortcut Trick
Initial average of 4 people (A, B, C, D) = 40 inches.
New average with E = 41 inches (increased by 1).
Height of E = 41 + (4 × 1) = 45 inches.
New average of (B, C, D, E, F) = 42 inches.
Sum of (B, C, D, F) = (Sum of B, C, D, E, F) − Height of E = (42 × 5) − 45 = 210 − 45 = 165 inches.
Average of (B, C, D, F) = 165 ÷ 4 = 41.25 inches.
∴ The correct answer is 41.25 inches.
Alternate Method
Given:
Average height (A+B+C+D) = 40 inches
Average height (A+B+C+D+E) = 41 inches
Average height (B+C+D+E+F) = 42 inches
Calculations:
⇒ Total height (A+B+C+D) = 40 × 4 = 160 inches
⇒ Total height (A+B+C+D+E) = 41 × 5 = 205 inches
⇒ Height of E = 205 − 160 = 45 inches
⇒ Total height (B+C+D+E+F) = 42 × 5 = 210 inches
⇒ Total height (B+C+D+F) = Total (B+C+D+E+F) − E = 210 − 45 = 165 inches
⇒ Average height (B+C+D+F) = 165 ÷ 4 = 41.25 inches
∴ The correct answer is 41.25 inches.
Additional Information
Average Calculation
Average = Sum of observations ÷ Number of observations.
Inclusion/Exclusion Rule
Value of new person = New Average + (Old Count × Change in Average).
Weighted Average
Total Sum = Sum1 + Sum2. Combined Average = (n1 × A1 + n2 × A2) ÷ (n1 + n2).
Ratio of alcohol and water in Y litres of mixture is 1 ∶ 4. (2/3)rd of the mixture is taken out and 250 ml of water is added to remaining mixture in such a way that the quantity of alcohol and water is final mixture become 4 ∶ 19. Find the value of Y.
4 litres
3 litres
2 litres
5 litres
1 litre
Correct answer
5 litres
Why this answer is correct
Shortcut Trick
Initial ratio Alcohol : Water = 1 : 4. Total units = 5.
After removing 2/3, remaining mixture is 1/3 of Y. Ratio stays 1 : 4.
In remaining part: Alcohol = 1x, Water = 4x. Add 250 ml water → 1x / (4x + 250) = 4 / 19.
⇒ 19x = 16x + 1000 ⇒ 3x = 1000 ⇒ x = 1000/3 ml.
Remaining mixture = 5x = 5000/3 ml. Original Y = 3 × (5000/3) = 5000 ml.
∴ The correct answer is 5 litres.
Alternate Method
Given: Initial Ratio = 1 : 4, Removed = 2/3, Added Water = 250 ml, Final Ratio = 4 : 19.
⇒ Let remaining mixture (Y/3) consist of Alcohol = a and Water = 4a.
⇒ New Alcohol : New Water = a : (4a + 250) = 4 : 19
⇒ 19 × a = 4 × (4a + 250)
⇒ 19a = 16a + 1000
⇒ 3a = 1000 ml ⇒ a = 1000/3 ml
⇒ Total remaining mixture (Y/3) = a + 4a = 5a
⇒ Y/3 = 5 × (1000/3) = 5000/3 ml
⇒ Y = 5000 ml = 5 litres
∴ The correct answer is 5 litres.
Additional Information
Mixture Withdrawal Rule
When a part of a mixture is removed, the ratio of components in the remaining mixture remains the same as the initial ratio.
Alligation Method
Used to find the ratio in which two ingredients are mixed to produce a desired concentration: (Cheaper) : (Dearer) = (d−m) : (m−c).
Replacement Formula
Final Quantity = Initial Quantity × (1 − x/V)n, where x is quantity replaced, V is total volume, and n is number of operations.
What approximate value will come in place of the question mark ‘?’ in the following question?
211.15 + 111.215 × 210.35 + 629.55 × 1.73 = ?
12345
23451
12786
24781
24356
Correct answer
24781
Why this answer is correct
Concept:
Follow BODMAS rule to solve this question, as per the order given below,
Step-1: Parts of an equation enclosed in Brackets must be solved first, and in the bracket, the BODMAS rule must be followed,
Step-2: Any mathematical Of or Exponent must be solved next,
Step-3: Next, the parts of the equation that contain Division and Multiplication are calculated
Step-4: Last but not least, the parts of the equation that contain Addition and Subtraction should be calculated.
Calculation:
211 + 111 × 210 + 630 × 2 = ?
⇒ 211 + 23310 + 1260 = ?
⇒ ? = 24781
What approximate value should come in the place of question mark (?) in the following question?
121.98 – [70.98 + {4.14 – (4.98 – (22.98 – 21.12))}] = ?
40
50
30
60
20
Correct answer
50
Why this answer is correct
Follow BODMAS rule to solve this question, as per the order given below.
Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -
Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.
Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.
Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Since, we need to find out the approximate value, we can write these values to their nearest integers.
Given expression is
121.98 – [70.98 + {4.14 – (4.98 – (22.98 – 21.12))}] = ?
⇒ 122 – [71 + {4 – (5 – (23 – 21))}] = ?
⇒ 122 – [71 + {4 – (5 – 2)}] = ?
⇒ 122 – [71 + {4 – 3}] = ?
⇒ 122 – [71 + 1] = ?
⇒ 122 – 72 = ?
⇒ 50 = ?
What approximate value will come in place of question mark (?) in the following question?
(64.98% of 400.01 + 33.06 × 21.918 – 743.018) = ?
207
225
216
243
238
Correct answer
243
Why this answer is correct
Concept:
Follow BODMAS rule to solve this question, as per the order given below.
Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -
Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.
Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.
Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Calculation:
Writing the approximate values to the nearest integer
(65% of 400 + 33 × 22 – 743) = ?
? = (65/100 × 400 + 726 – 743)
= 260 + 726 – 743
= 243
What approximate value should come in the place of question mark (?) in the following question?
49.9% of 499.9 × 19.9% of 99.9 ÷ ? = 49.9% of 1999.9
9
2
14
18
5
Correct answer
5
Why this answer is correct
Follow the BODMAS rule to solve this question, as per the order given below.
Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -
Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.
Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.
Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Since we need to find out the approximate value, we can write these values to their nearest integers.
Given Expression.
49.9% of 499.9 × 19.9% of 99.9 ÷ ? = 49.9% of 1999.9
⇒ 50% of 500 × 20% of 100 ÷ ? = 50% of 2000
⇒ 250 × 20 ÷ ? = 1000
⇒ ? = 5
What approximate value should come in the place of question mark (?) in the following question?
34.98% of 799.99 + 64.95% of 199.98 = ? + 49.99% of 249.99
285
295
275
225
245
Correct answer
285
Why this answer is correct
Follow BODMAS rule to solve this question, as per the order given below.
Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -
Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.
Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.
Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Since, we need to find out the approximate value, we can write these values to their nearest integers.
Given expression is
34.98% of 799.99 + 64.95% of 199.98 = ? + 49.99% of 249.99
⇒ 35% of 800 + 65% of 200 = ? + 50% of 250
⇒ 280 + 130 = ? + 125
⇒ 410 = ? + 125
∴ ? = 285
A boat goes from point A to B upstream and returns to A through the same path. If the time of journey from A to B is twice that of the time taken to travel from B to A, then the ratio of the speed of the boat in still water to the speed of the current is
2 ∶ 1
4 ∶ 3
3 ∶ 2
5 ∶ 4
3 ∶ 1
Correct answer
3 ∶ 1
Why this answer is correct
Shortcut Trick
Time ratio (Upstream : Downstream) = 2 : 1
Speed ratio (Upstream : Downstream) = 1 : 2 (Inverse of time)
Ratio of Still Water Speed : Current Speed = (D + U) : (D − U)
Ratio = (2 + 1) : (2 − 1) = 3 : 1
∴ The correct answer is 3 : 1.
Alternate Method
Given: Time taken upstream (A to B) = 2 × Time taken downstream (B to A).
Formula Used: Speed = Distance ÷ Time; Upstream Speed (U) = u − v; Downstream Speed (D) = u + v.
⇒ Let speed of boat in still water = u and speed of current = v.
⇒ Distance (d) is constant, so (u − v) × 2t = (u + v) × t.
⇒ 2u − 2v = u + v
⇒ 2u − u = v + 2v
⇒ u = 3v
⇒ u : v = 3 : 1
∴ The correct answer is 3 : 1.
Additional Information
Upstream and Downstream Speed
Downstream Speed (D) = u + v and Upstream Speed (U) = u − v, where u is boat speed and v is current speed.
Still Water Speed Calculation
The speed of the boat in still water (u) is the average of downstream and upstream speeds: u = (D + U) ÷ 2.
Current Speed Calculation
The speed of the current (v) is half the difference between downstream and upstream speeds: v = (D − U) ÷ 2.
Vishnu has some amount of money and he invested the money in two schemes X and Y in the ratio of 2 : 5 for 2 years, scheme X offers 30% pa compound interest and scheme Y offers 15% pa Simple interest. The difference between the interest earned from both the schemes is Rs. 10800. How much was invested in scheme Y?
4,00,000
4,20,000
3,90,000
4,80,000
4,50,000
Correct answer
4,50,000
Why this answer is correct
Shortcut Trick
Effective CI for 2 years at 30% = 30 + 30 + (30 × 30)/100 = 69%
Effective SI for 2 years at 15% = 15 × 2 = 30%
Let investments be 200u and 500u. Interest X = 200 × 69% = 138u; Interest Y = 500 × 30% = 150u
Difference = 150u − 138u = 12u → 10800. So, 1u = 900
Investment in Scheme Y = 500 × 900 = 4,50,000
∴ The correct answer is 4,50,000.
Alternate Method
Given: Ratio of investment X : Y = 2 : 5, Time = 2 years, Rate X = 30% (CI), Rate Y = 15% (SI), Difference in Interest = Rs. 10800.
Formula Used: CI = P[(1 + r/100)t − 1]; SI = (P × R × T) / 100
⇒ Let Investment in X = 200k and Y = 500k
⇒ Interest from X = 200k × [(1 + 30/100)2 − 1] = 200k × [1.69 − 1] = 200k × 0.69 = 138k
⇒ Interest from Y = (500k × 15 × 2) / 100 = 150k
⇒ Difference = 150k − 138k = 12k
⇒ 12k = 10800
⇒ k = 900
⇒ Investment in Scheme Y = 500 × 900 = 4,50,000
∴ The correct answer is 4,50,000.
Additional Information
Effective Rate for Compound Interest
For 2 years at rate r%, the effective CI rate is given by the formula (2r + r2/100)%.
Simple Interest vs Compound Interest
Simple Interest is calculated only on the principal, while Compound Interest is calculated on the principal plus the accumulated interest of previous periods.
Difference for 2 years
For the same principal and rate, the difference between CI and SI for 2 years is P × (R/100)2.
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.