Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
What value should replace the question mark (?) in the following expression?
24 × 15 − 18 × 12 + 45 = ?
199
209
179
189
195
Correct answer
189
Why this answer is correct
Given:
24 × 15 − 18 × 12 + 45 = ?
Calculation:
⇒ 360 − 216 + 45
⇒ 144 + 45
⇒ ? = 189
∴ The correct answer is 189.
What value should replace the question mark (?) in the following expression?
45% of 640 + 25% of 320 = ?
368
378
358
348
352
Correct answer
368
Why this answer is correct
Given:
45% of 640 + 25% of 320 = ?
Calculation:
⇒ ? = (45 × 640) ÷ 100 + (25 × 320) ÷ 100
⇒ ? = 288 + 80
⇒ ? = 368
∴ The correct answer is 368.
What value should replace the question mark (?) in the following expression?
(18)2 − (13)2 + √576 = ?
179
169
174
184
176
Correct answer
179
Why this answer is correct
Given:
(18)2 − (13)2 + √576 = ?
Calculation:
⇒ ? = 324 − 169 + 24
⇒ ? = 155 + 24
⇒ ? = 179
∴ The correct answer is 179.
What value should replace the question mark (?) in the following expression?
3/5 of 450 + 2/7 of 385 = ?
390
370
380
348
357
Correct answer
380
Why this answer is correct
Given:
3 ÷ 5 of 450 + 2 ÷ 7 of 385 = ?
Calculation:
⇒ ? = 3 × (450 ÷ 5) + 2 × (385 ÷ 7)
⇒ ? = 3 × 90 + 2 × 55
⇒ ? = 270 + 110
⇒ ? = 380
∴ The correct answer is 380.
What value should replace the question mark (?) in the following expression?
1250 ÷ 25 × 8 − 140 = ?
250
270
240
260
290
Correct answer
260
Why this answer is correct
Given:
1250 ÷ 25 × 8 − 140 = ?
Calculation:
⇒ 1250 ÷ 25 × 8 − 140
⇒ 50 × 8 − 140
⇒ 400 − 140
⇒ ? = 260
∴ The correct answer is 260.
What value should replace the question mark (?) in the following expression?
√1296 + √961 − √441 = ?
44
42
46
48
40
Correct answer
46
Why this answer is correct
Shortcut Trick
Identify square roots:
√1296 = 36, √961 = 31, and √441 = 21.
Substitute values into the expression: 36 + 31 − 21.
Calculate the result: 67 − 21 = 46.
∴ The correct answer is 46.
Alternate Method
Given:
√1296 + √961 − √441 = ?
Formula Used:
Square root simplification and BODMAS rule.
Calculations:
⇒ √1296 = 36 (as 36 × 36 = 1296)
⇒ √961 = 31 (as 31 × 31 = 961)
⇒ √441 = 21 (as 21 × 21 = 441)
⇒ ? = 36 + 31 − 21
⇒ ? = 67 − 21
⇒ ? = 46
∴ The correct answer is 46.
Additional Information
Square Root Estimation
To find √1296, note that 302 = 900 and 402 = 1600. Since the last digit is 6, the root must end in 4 or 6. Testing 36 gives 36 × 36 = 1296.
BODMAS Rule
The BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction) ensures that arithmetic operations are solved in the correct sequence.
Perfect Square Properties
A perfect square ending in 1 will have a square root ending in 1 or 9. For example, √961 ends in 1, leading to the estimate of 31.
What value should replace the question mark (?) in the following expression?
65% of 800 − 3/8 of 512 = ?
338
308
328
318
348
Correct answer
328
Why this answer is correct
Given:
65% of 800 - 3 ÷ 8 of 512 = ?
Calculation:
⇒ 65% of 800 = 65 × 8 = 520
⇒ (3 ÷ 8) × 512 = 3 × 64 = 192
⇒ ? = 520 - 192
⇒ ? = 328
∴ The correct answer is 328.
What value should replace the question mark (?) in the following expression?
12.5 × 16 + 37.5 × 8 − 100 = ?
400
410
380
390
430
Correct answer
400
Why this answer is correct
Given:
12.5 × 16 + 37.5 × 8 − 100 = ?
Calculation:
⇒ ? = 200 + 300 − 100
⇒ ? = 500 − 100
⇒ ? = 400
∴ The correct answer is 400.
Study the bar graph given below carefully and answer the questions that follow. The graph shows the number of mobile phones sold by five stores (A, B, C, D and E) in the years 2022 and 2023.
What is the total number of mobile phones sold by all five stores in the year 2022?
800
650
700
750
500
Correct answer
700
Why this answer is correct
Common Data
| Store | 2022 | 2023 |
|---|---|---|
| A | 120 | 150 |
| B | 150 | 180 |
| C | 180 | 150 |
| D | 90 | 120 |
| E | 160 | 200 |
Calculation:
Total phones sold in 2022 = 120 + 150 + 180 + 90 + 160
= 700
Therefore, the correct answer is 700 (Option C).
Study the bar graph given below carefully and answer the questions that follow. The graph shows the number of mobile phones sold by five stores (A, B, C, D and E) in the years 2022 and 2023.
What is the ratio of the phones sold by Store C in 2022 to the phones sold by Store E in 2023?
9 : 10
7 : 8
8 : 9
4 : 5
9 : 7
Correct answer
9 : 10
Why this answer is correct
Common Data
| Store | 2022 | 2023 |
|---|---|---|
| A | 120 | 150 |
| B | 150 | 180 |
| C | 180 | 150 |
| D | 90 | 120 |
| E | 160 | 200 |
Calculation:
Phones sold by Store C in 2022 = 180.
Phones sold by Store E in 2023 = 200.
Required ratio = 180 : 200
Dividing both terms by 20, required ratio = 9 : 10.
Therefore, the correct answer is 9 : 10 (Option A).
Study the bar graph given below carefully and answer the questions that follow. The graph shows the number of mobile phones sold by five stores (A, B, C, D and E) in the years 2022 and 2023.
What is the percentage increase in the sales of Store D from 2022 to 2023?
40%
30%
25%
33 1/3 %
0.28
Correct answer
33 1/3 %
Why this answer is correct
Common Data
| Store | 2022 | 2023 |
|---|---|---|
| A | 120 | 150 |
| B | 150 | 180 |
| C | 180 | 150 |
| D | 90 | 120 |
| E | 160 | 200 |
Calculation:
Increase in Store D's sales = 120 − 90 = 30.
Percentage increase = (30 / 90) × 100
= (1 / 3) × 100 = 33⅓%.
Therefore, the correct answer is 33⅓% (Option D).
Study the bar graph given below carefully and answer the questions that follow. The graph shows the number of mobile phones sold by five stores (A, B, C, D and E) in the years 2022 and 2023.
What is the average number of phones sold by all five stores in the year 2023?
165
155
150
160
170
Correct answer
160
Why this answer is correct
Common Data
| Store | 2022 | 2023 |
|---|---|---|
| A | 120 | 150 |
| B | 150 | 180 |
| C | 180 | 150 |
| D | 90 | 120 |
| E | 160 | 200 |
Calculation:
Total phones sold in 2023 = 150 + 180 + 150 + 120 + 200
= 800.
Average phones sold = 800 / 5 = 160.
Therefore, the correct answer is 160 (Option D).
Study the bar graph given below carefully and answer the questions that follow. The graph shows the number of mobile phones sold by five stores (A, B, C, D and E) in the years 2022 and 2023.
The phones sold by Store B in both years together are what percent of the total phones sold by all the stores in both years together?
22%
20%
24%
25%
0.28
Correct answer
22%
Why this answer is correct
Common Data
| Store | 2022 | 2023 |
|---|---|---|
| A | 120 | 150 |
| B | 150 | 180 |
| C | 180 | 150 |
| D | 90 | 120 |
| E | 160 | 200 |
Calculation:
Store B's sales in both years = 150 + 180 = 330.
Total sales by all stores in both years = 700 + 800 = 1500.
Required percentage = (330 / 1500) × 100
= 22%.
Therefore, the correct answer is 22% (Option A).
A can complete a piece of work in 10 days and B can complete the same work in 15 days. Both started working together, but B left after 3 days. The remaining work was completed by A alone. In how many days was the whole work completed?
8 days
7 days
9 days
10 days
6 days
Correct answer
8 days
Why this answer is correct
Shortcut Trick
Total work = LCM(10, 15) = 30 units.
Efficiency: A = 3 units/day, B = 2 units/day.
Work done by B in 3 days = 2 × 3 = 6 units.
Remaining work (30 − 6 = 24 units) was completed by A over the entire duration.
Total time for whole work = Total work done by A ÷ Efficiency of A = 24 ÷ 3 = 8 days.
∴ The correct answer is 8 days.
Alternate Method
Given: A completes work in 10 days, B in 15 days. They work together for 3 days.
Formula: Efficiency = Total Work ÷ Time
| Person | Days | Total Work | Efficiency |
|---|---|---|---|
| A | 10 | 30 (LCM) | 3 |
| B | 15 | 2 |
⇒ Combined Efficiency of A and B = 3 + 2 = 5 units/day.
⇒ Work done by (A + B) in 3 days = 5 × 3 = 15 units.
⇒ Remaining work = Total Work − Work Done = 30 − 15 = 15 units.
⇒ Time taken by A to complete remaining work = 15 ÷ 3 = 5 days.
⇒ Total days to complete whole work = 3 days (together) + 5 days (A alone) = 8 days.
∴ The correct answer is 8 days.
Additional Information
Pipes and Cisterns
It follows the same logic as Time & Work, where filling pipes have positive efficiency and emptying (leakage) pipes have negative efficiency.
Work and Wages
Wages are distributed among workers in the ratio of the actual work completed by each individual (Efficiency × Time).
Efficiency Relation
If efficiency is increased by x%, the time taken decreases. Time and Efficiency are inversely proportional for a constant amount of work.
The marked price of an article is 40% above its cost price. The shopkeeper allows a discount of 25% on the marked price. If the difference between the marked price and the selling price is Rs. 210, then what is the cost price of the article?
Rs. 600
Rs. 540
Rs. 720
Rs. 640
Rs. 580
Correct answer
Rs. 600
Why this answer is correct
Shortcut Trick
Difference between MP and SP is always the Discount amount.
Discount = 25% of MP = ₹210 ⇒ MP = 210 × 4 = ₹840.
MP is 40% above CP ⇒ 140% of CP = 840.
CP = 840 ÷ 1.4 = ₹600.
∴ The correct answer is ₹600.
Alternate Method
Given:
Markup % = 40% above CP
Discount % = 25% on MP
Difference (MP − SP) = ₹210
Formula Used:
MP = CP × (100 + Markup%)/100
SP = MP × (100 − Discount%)/100
Discount = MP − SP
CP (100%) Marked Price (140%) Discount (25%) Difference (MP − SP) = ₹210
Calculations:
⇒ Let Cost Price (CP) = 100 units
⇒ Marked Price (MP) = 100 + 40% of 100 = 140 units
⇒ Discount = 25% of MP = 25% of 140 = 35 units
⇒ Selling Price (SP) = MP − Discount = 140 − 35 = 105 units
⇒ Difference between MP and SP = 140 − 105 = 35 units
⇒ Given:
35 units = ₹210
⇒ 1 unit = 210 ÷ 35 = ₹6
⇒ Cost Price (CP) = 100 units = 100 × 6 = ₹600
∴ The correct answer is ₹600.
Additional Information
Markup and Discount Relation
Profit % = Markup % − Discount % − (Markup % × Discount %)/100. This is the effective percentage change from CP to SP.
CP and MP Ratio
CP/MP = (100 − Discount%)/(100 + Profit%). This direct ratio helps find CP or MP when profit and discount percentages are known.
Successive Discounts
If two successive discounts d1 and d2 are given, the single equivalent discount = d1 + d2 − (d1 × d2)/100.
Verified Answer: Rs. 600
Six years ago, the ratio of the ages of A and B was 3 : 4. The present age of C is 16 years. Four years hence, the ratio of the ages of B and C will be 3 : 2. What is the present age of A?
21 years
19 years
22 years
20 years
25 years
Correct answer
21 years
Why this answer is correct
Shortcut Trick
Work backwards from C: C (4 yrs later) = 16 + 4 = 20 years.
B (4 yrs later) = (3 ÷ 2) × 20 = 30 years.
B (6 yrs ago) = 30 − 4 (to present) − 6 (to past) = 20 years.
A (6 yrs ago) = (3 ÷ 4) × 20 = 15 years.
A (Present) = 15 + 6 = 21 years.
∴ The correct answer is 21 years.
Alternate Method
Given:
Present age of C = 16 years.
Ratio of A : B (6 years ago) = 3 : 4.
Ratio of B : C (4 years hence) = 3 : 2.
Formula Used:
Value = (Ratio Part ÷ Other Ratio Part) × Known Value
6 yrs ago Present 4 yrs hence C = 20 B = 30 C = 16 B = 26 B = 20 A = 15 Total Gap = 10 yrs
⇒ Present Age of C = 16 years
⇒ Age of C (4 years hence) = 16 + 4 = 20 years
⇒ Ratio B : C (4 years hence) = 3 : 2
⇒ 2 parts = 20 ∴ 1 part = 10
⇒ Age of B (4 years hence) = 3 × 10 = 30 years
⇒ Age of B (6 years ago) = 30 − 4 (future to present) − 6 (present to past) = 20 years
⇒ Ratio A : B (6 years ago) = 3 : 4
⇒ 4 parts = 20 ∴ 1 part = 5
⇒ Age of A (6 years ago) = 3 × 5 = 15 years
⇒ Present Age of A = 15 + 6 = 21 years
∴ The correct answer is 21 years.
Additional Information
Constant Age Difference
The difference between the ages of two individuals always remains the same, regardless of how many years in the past or future are considered.
Age Ratio Shifting
To shift a ratio from 'n' years ago to present, you must find the values first, then add 'n'. Direct addition to ratio parts is mathematically incorrect.
Ratio Unitary Method
Value per unit = Total Value ÷ Total units. Individual value = Units × Value per unit.
P and Q started a business. The investment of P is 250% more than that of Q and the ratio of time period of P's investment and Q's investment is 8 : 7. If Q got Rs 3200 as his share of Profit, then what is the total profit earned by them?
Rs 16000
Rs 20000
Rs 12000
Rs 32000
Rs 24000
Correct answer
Rs 16000
Why this answer is correct
Suppose Q invested Rs 100P for 7m months.
Then P's investment in Rs 350P for 8m months.
Ratio of investment of P and Q = (350P× 8M ) : ( 100P ×7M )
⇒ 2800Pm : 700pm = 4 : 1
Now Q, share is Rs 3200
⇒ 1 unit = Rs 3200
Total profit is equal to 5unit
⇒ Rs 3200×5 = Rs 16000
Hence Rs 16000 is the correct answer.
Find the missing number in each of the following series.
7, 14, 28, 56, ?, 224
98
112
106
118
124
Correct answer
112
Why this answer is correct
Given:
7, 14, 28, 56, ?, 224
Pattern used:
Previous term × 2
Calculation:
⇒ 7 × 2 = 14
⇒ 14 × 2 = 28
⇒ 28 × 2 = 56
⇒ 56 × 2 = 112
⇒ 112 × 2 = 224
∴ The correct answer is 112.
Find the missing number in each of the following series.
5, 6, 14, 45, ?, 925
194
164
184
174
154
Correct answer
184
Why this answer is correct
Given:
Series:
5, 6, 14, 45, ?, 925
Pattern used:
(Previous term × n) + n, where n starts from 1.
Calculation:
⇒ 5 × 1 + 1 = 6
⇒ 6 × 2 + 2 = 14
⇒ 14 × 3 + 3 = 45
⇒ 45 × 4 + 4 = 184
⇒ 184 × 5 + 5 = 925
∴ The correct answer is 184.
Find the missing number in each of the following series.
8, 12, 24, 60, ?, 630
195
180
150
165
170
Correct answer
180
Why this answer is correct
Given:
8, 12, 24, 60, ?, 630
Pattern used:
Multiplication by 1.5, 2.0, 2.5, 3.0, 3.5
Calculation:
⇒ 8 × 1.5 = 12
⇒ 12 × 2.0 = 24
⇒ 24 × 2.5 = 60
⇒ 60 × 3.0 = 180
⇒ 180 × 3.5 = 630
∴ The correct answer is 180.
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.