Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
In each of the following number series, the wrong number is given, find out that number.
23, 45, 89, 167, 353, 705
167
353
89
45
705
Correct answer
167
Why this answer is correct
The series follows the following pattern:
23 × 2 - 1 = 45
45 × 2 - 1 = 89
89 × 2 - 1 = 177
177 × 2 - 1 = 353
353 × 2 - 1 = 705
∴ The wrong term in the series is 167.
In each of the following number series, the wrong number is given, find out that number.
1128, 1120, 1093, 1029, 904, 788
1120
904
788
1029
1093
Correct answer
788
Why this answer is correct
The series follows the following pattern:
1128 – 23 = 1120
1120 – 33 = 1093
1093 – 43 = 1029
1029 – 53 = 904
904 – 63 = 688
∴ The wrong term in the series is 788.
In each of the following number series, the wrong number is given, find out that number.
112, 116, 126, 140, 172, 236
116
126
140
236
172
Correct answer
126
Why this answer is correct
The series follows the following pattern:
112 + 4 = 116
116 + 8 = 124
124 + 16 = 140
140 + 32 = 172
172 + 64 = 236
∴ The wrong term in the series is 126.
In a mixture of 30 litres, alcohol and water are in the ratio of 3 : 2. If 20 litres of mixture is removed and then 15 litres of alcohol and 10 litres of water is added to the mixture. What is the ratio of alcohol and water in the new mixture?
2 : 3
3 : 2
3 : 5
5 : 3
None of these
Correct answer
3 : 2
Why this answer is correct
Shortcut Trick
Initial mixture = 30 litres, Removed = 20 litres, Remaining = 10 litres.
Ratio in remaining 10 litres is still 3 : 2 → Alcohol = 6 litres, Water = 4 litres.
New Alcohol = 6 + 15 = 21 litres; New Water = 4 + 10 = 14 litres.
New Ratio = 21 : 14 = 3 : 2.
∴ The correct answer is 3 : 2.
Alternate Method
Given: Initial Volume = 30 litres, Ratio A:W = 3:2, Removed = 20 litres, Added = 15L Alcohol & 10L Water.
⇒ Remaining mixture = 30 − 20 = 10 litres.
⇒ Alcohol in 10 litres = (3/5) × 10 = 6 litres.
⇒ Water in 10 litres = (2/5) × 10 = 4 litres.
⇒ New Alcohol amount = 6 + 15 = 21 litres.
⇒ New Water amount = 4 + 10 = 14 litres.
⇒ New Ratio = 21 : 14 = 3 : 2.
∴ The correct answer is 3 : 2.
Additional Information
Ratio Stability Principle
When a part of a homogeneous mixture is removed, the ratio of components in the remaining portion and the removed portion remains the same as the original mixture.
Alligation Rule
It is used to find the ratio in which two or more ingredients at the given price/concentration must be mixed to produce a mixture of a desired price/concentration.
The ratio of the length and breadth of a rectangle is 7 : 6. If the height of the cylinder is equal to the length of the rectangle and radius of the cylinder is 21 cm and the curved surface area of the cylinder is 1848 sq cm. Then find the perimeter of rectangle ?
52 cm
48 cm
46 cm
42 cm
56cm
Correct answer
52 cm
Why this answer is correct
Shortcut Trick
Curved Surface Area (CSA) = 2πrh ⇒ 1848 = 2 × (22/7) × 21 × Height.
Height (h) = 1848 ÷ (2 × 22 × 3) = 1848 ÷ 132 = 14 cm.
Length (L) = Height = 14 cm. Since Ratio L:B = 7:6, then 7 units = 14 cm → 1 unit = 2 cm.
Breadth (B) = 6 × 2 = 12 cm. Perimeter = 2(L + B) = 2(14 + 12) = 2 × 26 = 52 cm.
∴ The correct answer is 52 cm.
Alternate Method
Given: Ratio L:B = 7:6, Radius (r) = 21 cm, CSA = 1848 sq cm, Height (h) = Length (L).
Formula Used: Curved Surface Area = 2πrh; Perimeter = 2(L + B).
⇒ 1848 = 2 × (22/7) × 21 × h
⇒ 1848 = 132 × h
⇒ h = 1848 ÷ 132 = 14 cm
⇒ Length (L) = 14 cm
⇒ Since 7x = 14, then x = 2
⇒ Breadth (B) = 6 × 2 = 12 cm
⇒ Perimeter = 2 × (14 + 12) = 2 × 26 = 52 cm
∴ The correct answer is 52 cm.
Additional Information
Cylinder Properties
Total Surface Area (TSA) = 2πr(r + h) and Volume = πr2h.
Rectangle Formulas
Area = Length × Breadth and Diagonal = √(L2 + B2).
Under a new scheme, a bank offers an interest of 20% per annum compounded annually. Suraj deposits Rs. 10,000 under this scheme and at the end, he receives Rs. 12000. What was the tenure of the scheme that Suraj had chosen?
1 year
2 years
3 years
4 years
None of these
Correct answer
1 year
Why this answer is correct
Shortcut Trick
Rate = 20% p.a. ⇒ Multiplier = 1.20
Amount = Principal × (Multiplier)n
12000 = 10000 × (1.2)n ⇒ 1.2 = (1.2)n
Comparing powers, n = 1.
∴ The correct answer is 1 year.
Alternate Method
Given: Principal (P) = ₹10,000, Amount (A) = ₹12,000, Rate (R) = 20%
Formula Used: A = P(1 + R/100)n
⇒ 12000 = 10000(1 + 20/100)n
⇒ 12000/10000 = (1 + 1/5)n
⇒ 1.2 = (6/5)n
⇒ 1.2 = (1.2)n
⇒ n = 1
∴ The correct answer is 1 year.
Additional Information
Compound Interest Formula
The total amount A = P(1 + r/n)nt, where P is principal, r is annual interest rate, n is compounding frequency, and t is time.
Effective Rate for 1 Year
When compounded annually, the effective rate is the same as the nominal rate for the first year. CI = SI for the 1st year.
Half-yearly Compounding
Rate is halved (R/2) and time is doubled (2n) when interest is calculated semi-annually.
The average weight of A, B and C is 50kg, the average weight of C, D and E is 70kg and the average weight of A, B and E is 53 (1/3)kg. The average weight of E and C is 65kg and B’s weight is 10kg less than C’s weight. Find the weight of A.
48 kg
40 kg
45 kg
50 kg
55 kg
Correct answer
40 kg
Why this answer is correct
Shortcut Trick
Total weight (A+B+C) = 50 × 3 = 150 kg
Total weight (C+D+E) = 70 × 3 = 210 kg
Total weight (A+B+E) = 53(1/3) × 3 = 160 kg
Total weight (E+C) = 65 × 2 = 130 kg
From (A+B+C) and (A+B+E): C − E = 150 − 160 = −10 ⇒ E − C = 10
Solve E + C = 130 and E − C = 10 ⇒ C = 60 kg, B = C − 10 = 50 kg, A = 150 − (50 + 60) = 40 kg
∴ The correct answer is 40 kg.
Alternate Method
Given: Average (A,B,C) = 50, Average (C,D,E) = 70, Average (A,B,E) = 160/3, Average (E,C) = 65, B = C − 10
⇒ A + B + C = 3 × 50 = 150 --- (Eq. 1)
⇒ A + B + E = 3 × 160/3 = 160 --- (Eq. 2)
⇒ E + C = 2 × 65 = 130 --- (Eq. 3)
⇒ Subtract (Eq. 1) from (Eq. 2): (A + B + E) − (A + B + C) = 160 − 150
⇒ E − C = 10 --- (Eq. 4)
⇒ Adding (Eq. 3) and (Eq. 4): 2E = 140 ⇒ E = 70 kg
⇒ Substituting E in (Eq. 3): 70 + C = 130 ⇒ C = 60 kg
⇒ Weight of B = C − 10 = 60 − 10 = 50 kg
⇒ Substituting B and C in (Eq. 1): A + 50 + 60 = 150
⇒ A + 110 = 150 ⇒ A = 40 kg
∴ The correct answer is 40 kg.
Additional Information
Average Formula
Average = (Sum of all observations) ÷ (Total number of observations). Sum = Average × Number of items.
Weighted Average
When two groups with averages A1 and A2 and sizes n1 and n2 are combined, the new average is (n1A1 + n2A2) ÷ (n1 + n2).
Net Deviation Method
The sum of deviations of all items from the actual average is always zero. This is used for faster calculation in complex average problems.
What will come in the place of the question mark ‘?’ in the following question?
15 × √16 – 30% of 200 = 25% of 80 + ? × 20
-1
-4
-5
0
None of these.
Correct answer
-1
Why this answer is correct
Given:
15 × √16 – 30% of 200 = 25% of 80 + ? × 20
Concept used:
Follow the BODMAS rule according to the table given below:
Calculation:
15 × √16 – 30% of 200 = 25% of 80 + ? × 20
⇒ 15 × 4 – (30/100) × 200 = (25/100) × 80 + ? × 20
⇒ 60 - 60 = 20 + ? × 20
⇒ 0 - 20 = ? × 20
⇒ ? = -20/20 = -1
∴ The value of ? is -1
What will come in the place of the question mark ‘?’ in the following question?
√1225 ÷ ∛343 × 45% of 760 = ? × 66.67% of 45
70
64
39
57
45
Correct answer
57
Why this answer is correct
Given:
√1225 ÷ ∛343 × 45% of 760 = ? × 66.67% of 45
Concept Used:
Follow BODMAS rule to solve this question, as per the order given below.
Calculation:
√1225 ÷ ∛343 × 45% of 760 = ? × 66.67% of 45
⇒ (35/7) × (45/100) × 760 = ? × (2/3) × 45
⇒ (35/7) × 342 = ? × 30
⇒ ? = 1710/30
⇒ ? = 57
∴ The value of (?) is 57.
What will come in the place of the question mark ‘?’ in the following question?
60% of 320 + 50% of 190 - 57% of 350 = ?
82.5
62.5
87.5
92.5
77.5
Correct answer
87.5
Why this answer is correct
Given:
60% of 320 + 50% of 190 - 57% of 350 = ?
Concept Used:
Calculation:
60% of 320 + 50% of 190 - 57% of 350 = ?
⇒ 192 + 95 - 199.5
⇒ ? = 87.5
∴ The value of (?) is 87.5
What should come in place of the question mark (?) in the following question?
165 ÷ 15 × 13 + (2/7) of 91 - ? = 50% of 320
5
6
7
8
9
Correct answer
9
Why this answer is correct
Given:
165 ÷ 15 × 13 + (2/7) of 91 - ? = 50% of 320
Concept used:
Follow the BODMAS rule according to the table given below:
Calculation:
165 ÷ 15 × 13 + (2/7) of 91 - ? = 50% of 320
⇒ 143 + (2/7) × 91 - ? = (50/100) × 320
⇒ 143 + 26 - ? = 1/2 × 320
⇒ 143 + 26 - ? = 160
⇒ 169 - ? = 160
⇒ ? = 9
∴ 9 should come in place of the question mark (?).
What will come in the place of the question mark ‘?’ in the following question?
45% of 300 – (?)2 = 56% of 75 – 10% of 510
18
14
16
12
19
Correct answer
12
Why this answer is correct
Given:
45% of 300 – (?)2 = 56% of 75 – 10% of 510
Concept Used:
Calculation:
45% of 300 – (?)2 = 56% of 75 – 10% of 510
⇒ 45 × 3 – (?)2 = 14 × 3 – 51
⇒ ?2 = (45 × 3) + 51 – (14 × 3)
⇒ ? = √144
⇒ ? = 12
∴ The value of (?) is 12.
Three friends started a business that offers them a profit of 25% of their total initial investment. They can’t withdraw their investments until the end of their business. Find the amount invested (in Rs) by Ajay if he invested Rs. 4,000 more than Rishi while Rishi and Samar invested the same amount, and Ajay got a profit share of Rs. 5000.
Rs. 22000
Rs. 20000
Rs. 25000
Rs. 35000
Rs. 15000
Correct answer
Rs. 20000
Why this answer is correct
Shortcut Trick
Since Profit % is same for all, Profit ratio is equal to Investment ratio.
Ajay Profit = 5000 ⇒ Ajay Investment × 25% = 5000.
Ajay Investment = 5000 ÷ 0.25 = 20000.
∴ The correct answer is Rs. 20000.
Alternate Method
Given: Profit % = 25%, Ajay Profit = Rs. 5000, Ajay Investment = Rishi + 4000, Rishi Investment = Samar Investment.
Formulas: Profit = Investment × Profit Percentage | Total Profit = ∑ Individual Profits.
Step 1: Let Ajay's Investment be Rs. A.
Step 2: Ajay's Profit = 25% of Ajay's Investment.
Step 3: 5000 = (25 ÷ 100) × A.
Step 4: A = (5000 × 100) ÷ 25.
Step 5: A = 5000 × 4 = 20000.
∴ The correct answer is Rs. 20000.
Additional Information
Partnership Profit Distribution
When the time period is same for all partners, the Profit is distributed in the ratio of their Initial Investments.
Investment Calculation
Individual Investment = Individual Profit ÷ Rate of Profit. In this case, Rishi and Samar's investments are (20000 − 4000) = 16000 each.
The efficiency of radha is 50% more than that of shyam. Total work is 240 units.
Quantity I: Find the number of days radha alone will take to complete 200% of the work?
Quantity II: Find the number of days radha and shyam together will take to complete 50% of the work?
Quantity 1 > Quantity 2
Quantity 1 ≥ Quantity 2
Quantity 1 < Quantity 2
Quantity 1 ≤ Quantity 2
Quantity 1 = Quantity 2
Correct answer
Quantity 1 > Quantity 2
Why this answer is correct
Shortcut Trick
Efficiency ratio Radha : Shyam = 150 : 100 = 3 : 2.
Quantity I: Work = 200% of 240 = 480 units. Time = 480 ÷ 3 = 160 days.
Quantity II: Work = 50% of 240 = 120 units. Combined Efficiency = 3 + 2 = 5. Time = 120 ÷ 5 = 24 days.
Clearly, 160 days > 24 days, so Quantity I > Quantity II.
∴ The correct answer is Quantity 1 > Quantity 2.
Alternate Method
Given: Total work = 240 units. Efficiency of Radha is 50% more than Shyam.
Formula Used: Time = Total Work ÷ Efficiency
Person
Efficiency Calculation
Efficiency Value
Shyam
Assume base efficiency
2 units/day
Radha
2 × 150%
3 units/day
Step 1: Calculate Quantity I
⇒ Target work = 240 × 200% = 480 units
⇒ Time taken by Radha = 480 ÷ 3
⇒ Quantity I = 160 days
Step 2: Calculate Quantity II
⇒ Target work = 240 × 50% = 120 units
⇒ Combined efficiency (Radha + Shyam) = 3 + 2 = 5 units/day
⇒ Time taken together = 120 ÷ 5
⇒ Quantity II = 24 days
⇒ Comparison: 160 > 24
∴ The correct answer is Quantity 1 > Quantity 2.
Additional Information
Work and Efficiency Relation
Efficiency is inversely proportional to time taken when work is constant. If efficiency ratio is a:b, time ratio is b:a.
Percentage in Work
Work done is directly proportional to the percentage of total units assigned. 200% work means doubling the initial units.
Combined Efficiency
When two or more people work together, their individual efficiencies (work done per day) are added to find the total rate of work.
In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.
A train of some length travelling at the speed of 108 km per hour can cross a pole on a platform in 25 seconds but at the speed of 90 km per hour it can cross a platform of x meters long in 40 seconds.
Quantity I: What is the length of the train?
Quantity II: What is the length of the platform?
Quantity 1 > Quantity 2
Quantity 1 ≥ Quantity 2
Quantity 1 < Quantity 2
Quantity 1 ≤ Quantity 2
Quantity 1 = Quantity 2
Correct answer
Quantity 1 > Quantity 2
Why this answer is correct
Shortcut Trick
Quantity I: Speed = 108 kmph = 108 × (5/18) = 30 m/s. Length = Speed × Time = 30 × 25 = 750 m.
Quantity II: Speed = 90 kmph = 90 × (5/18) = 25 m/s. Total distance = 25 × 40 = 1000 m.
Platform (x) = Total Distance − Train Length = 1000 − 750 = 250 m.
Comparing 750 m and 250 m, Quantity I > Quantity II.
∴ The correct answer is Quantity 1 > Quantity 2.
Alternate Method
Given: Speed1 = 108 kmph, Time1 = 25 s, Speed2 = 90 kmph, Time2 = 40 s.
Formula Used: Distance = Speed × Time; kmph to m/s conversion = × 5/18.
Quantity I (Train Length):
⇒ Speed in m/s = 108 × (5/18) = 30 m/s
⇒ Length of Train (L) = Speed × Time = 30 × 25
⇒ L = 750 m
Quantity II (Platform Length x):
⇒ Speed in m/s = 90 × (5/18) = 25 m/s
⇒ Total Distance = Speed × Time = 25 × 40 = 1000 m
⇒ Platform length (x) = 1000 − Train Length = 1000 − 750
⇒ x = 250 m
⇒ Comparison: 750 m > 250 m
∴ The correct answer is Quantity 1 > Quantity 2.
Additional Information
Relative Speed
When two objects move in the same direction, relative speed is the difference (S1 − S2); in opposite directions, it is the sum (S1 + S2).
Crossing Stationary Objects
To cross a pole or point object, distance = train length. To cross a platform or bridge, distance = train length + object length.
Unit Conversion
Convert km/h to m/s by multiplying by 5/18. Convert m/s to km/h by multiplying by 18/5.
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.