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Question 1Quantitative Aptitude

A shopkeeper marks an article at ₹1,200 and allows a discount of 15% on the marked price. What is the selling price?

  1. ₹1,050
  2. ₹1,150
  3. ₹1,080
  4. ₹1,020 Correct answer.

Explanation

A discount of 15% is calculated on the marked price, so the reduction is 15% of 1200 = 180. Subtracting gives 1200 − 180 = 1020. Equivalently, the selling price is 85% of 1200 = 1020.

Question 2Quantitative Aptitude

The average of five numbers is 28. If one number, 40, is removed, what is the average of the remaining four numbers?

  1. 25 Correct answer.
  2. 30
  3. 27
  4. 26

Explanation

The total of the five numbers is 5 × 28 = 140. Removing 40 leaves 100, which is spread over four numbers, giving 100 ÷ 4 = 25.

Question 3Quantitative Aptitude

A train 150 m long crosses a pole in 9 seconds. What is its speed in km/h?

  1. 54
  2. 50
  3. 60 Correct answer.
  4. 66

Explanation

Crossing a pole means covering the train's own length, so speed = 150 ÷ 9 = 16.67 m/s. Multiplying by 18/5 converts to km/h: 16.67 × 3.6 = 60 km/h.

Question 4Quantitative Aptitude

What is the value of 0.4 × 0.04 × 0.004 expressed as a decimal?

  1. 0.0064
  2. 0.000064 Correct answer.
  3. 0.064
  4. 0.00064

Explanation

Multiply the significant digits: 4 × 4 × 4 = 64. The decimal places total 1 + 2 + 3 = 6, so the product is 0.000064.

Question 5Quantitative Aptitude

If 40% of a number is 96, what is 75% of that number?

  1. 150
  2. 180 Correct answer.
  3. 200
  4. 160

Explanation

If 40% equals 96, then 1% equals 96 ÷ 40 = 2.4, so the whole number is 240. Then 75% of 240 = 180.

Question 6Quantitative Aptitude

The simple interest on ₹8,000 at 6% per annum for 2 years is:

  1. ₹960 Correct answer.
  2. ₹1,000
  3. ₹480
  4. ₹900

Explanation

Simple interest is P × R × T ÷ 100 = 8000 × 6 × 2 ÷ 100. This equals 960.

Question 7Quantitative Aptitude

Which of the following is the smallest fraction?

  1. 3/5
  2. 9/16
  3. 5/8
  4. 7/12 Correct answer.

Explanation

Convert to decimals: 3/5 = 0.6, 5/8 = 0.625, 7/12 ≈ 0.583, 9/16 = 0.5625. Comparing these, 7/12 is the smallest of the four values.

Question 8Quantitative Aptitude

A number leaves a remainder of 3 when divided by 7. What remainder does three times that number leave when divided by 7?

  1. 6
  2. 3
  3. 5
  4. 2 Correct answer.

Explanation

Let the number be 7q + 3. Three times it is 21q + 9 = 7(3q + 1) + 2, so the remainder is 2. Alternatively, 3 × 3 = 9 leaves remainder 2 on division by 7.

Question 9Quantitative Aptitude

The ratio of two numbers is 3:5 and their sum is 96. What is the smaller number?

  1. 40
  2. 48
  3. 60
  4. 36 Correct answer.

Explanation

The total of the ratio parts is 3 + 5 = 8, so one part equals 96 ÷ 8 = 12. The smaller number is 3 × 12 = 36.

Question 10Quantitative Aptitude

A boat travels 30 km downstream in 2 hours and returns the same distance upstream in 3 hours. What is the speed of the stream?

  1. 2.5 km/h Correct answer.
  2. 3 km/h
  3. 2 km/h
  4. 5 km/h

Explanation

Downstream speed is 30 ÷ 2 = 15 km/h and upstream speed is 30 ÷ 3 = 10 km/h. The stream speed is half the difference: (15 − 10) ÷ 2 = 2.5 km/h.

Question 11Quantitative Aptitude

A alone can complete a piece of work in 12 days and B alone in 18 days. Working together, in how many days will they finish the work?

  1. 6.5 days
  2. 7.5 days
  3. 8 days
  4. 7.2 days Correct answer.

Explanation

A does 1/12 of the work per day and B does 1/18. Together they do 3/36 + 2/36 = 5/36 per day, so the time needed is 36/5 = 7.2 days.

Question 12Quantitative Aptitude

A sum of money doubles itself in 8 years at simple interest. In how many years will it become four times itself at the same rate?

  1. 16 years
  2. 20 years
  3. 24 years Correct answer.
  4. 32 years

Explanation

Doubling means the interest equals the principal in 8 years, so the annual rate is 100/8 = 12.5%. To become four times, the interest must be three times the principal, requiring 3 × 8 = 24 years.

Question 13Quantitative Aptitude

The compound interest on ₹5,000 at 10% per annum for 2 years, compounded annually, is:

  1. ₹1,100
  2. ₹1,025
  3. ₹1,050 Correct answer.
  4. ₹1,000

Explanation

The amount after 2 years is 5000 × (1.1)² = 5000 × 1.21 = 6050. Compound interest is therefore 6050 − 5000 = 1050.

Question 14Quantitative Aptitude

A mixture contains milk and water in the ratio 5:3. If 8 litres of water are added, the ratio becomes 5:4. What was the original quantity of milk?

  1. 40 litres Correct answer.
  2. 32 litres
  3. 48 litres
  4. 56 litres

Explanation

Let milk be 5x and water 3x. Adding 8 litres of water gives 3x + 8 = 4x, so x = 8. The original milk quantity is 5 × 8 = 40 litres.

Question 15Quantitative Aptitude

The difference between the compound interest and simple interest on a sum at 10% per annum for 2 years is ₹50. What is the sum?

  1. ₹5,000 Correct answer.
  2. ₹4,000
  3. ₹6,000
  4. ₹5,500

Explanation

For two years the difference equals the interest on the first year's interest, i.e. P × (R/100)². So 50 = P × 0.01, giving P = 5000.

Question 16Quantitative Aptitude

A pipe fills a tank in 6 hours, while a second pipe empties it in 9 hours. If both are opened together when the tank is empty, how long will it take to fill?

  1. 18 hours Correct answer.
  2. 15 hours
  3. 12 hours
  4. 20 hours

Explanation

The filling rate is 1/6 per hour and the emptying rate is 1/9 per hour. The net rate is 3/18 − 2/18 = 1/18 per hour, so the tank fills in 18 hours.

Question 17Quantitative Aptitude

A sum invested at compound interest amounts to ₹8,820 in 2 years and ₹9,261 in 3 years. What is the rate of interest per annum?

  1. 4%
  2. 7%
  3. 5% Correct answer.
  4. 6%

Explanation

The interest for the third year alone is 9261 − 8820 = 441. As a fraction of the amount at the start of that year, 441/8820 = 0.05, so the rate is 5% per annum.

Question 18Quantitative Aptitude

What is the value of (√1764 + √441) ÷ √49?

  1. 7 Correct answer.
  2. 5
  3. 3
  4. 9

Explanation

Since 42² = 1764, √1764 = 42; since 21² = 441, √441 = 21; and √49 = 7. Thus (42 + 21) ÷ 7 = 63 ÷ 7 = 9.

Question 19Quantitative Aptitude

The perimeter of a rectangle is 60 cm and its length is 4 cm more than its breadth. What is the area of the rectangle?

  1. 210 cm²
  2. 200 cm²
  3. 221 cm² Correct answer.
  4. 216 cm²

Explanation

Let breadth be b and length b + 4. Then 2(b + b + 4) = 60, so 2b + 4 = 30 and b = 13, giving length 17. The area is 13 × 17 = 221 cm².

Question 20Quantitative Aptitude

A circle has circumference 44 cm. Taking π = 22/7, what is its area?

  1. 132 cm²
  2. 154 cm² Correct answer.
  3. 144 cm²
  4. 176 cm²

Explanation

From 2πr = 44, we get 2 × 22/7 × r = 44, so r = 7 cm. The area is πr² = 22/7 × 49 = 154 cm².

Question 21Quantitative Aptitude

A sum of ₹12,000 is invested partly at 8% and the rest at 12% simple interest per annum. If the total annual interest is ₹1,160, how much is invested at 12%?

  1. ₹5,000 Correct answer.
  2. ₹6,000
  3. ₹7,000
  4. ₹4,000

Explanation

Let x be the amount at 12%. Then 0.08(12000 − x) + 0.12x = 1160, giving 960 + 0.04x = 1160, so 0.04x = 200 and x = 5000.

Question 22Quantitative Aptitude

A and B start a business with capitals in the ratio 4:5. After 6 months A withdraws his entire capital, while B continues for the full year. If the total annual profit is ₹4,400, what is B's share?

  1. ₹2,800 Correct answer.
  2. ₹2,400
  3. ₹2,000
  4. ₹1,600

Explanation

Profit shares depend on capital × time. A's contribution is 4 × 6 = 24 units and B's is 5 × 12 = 60 units, so the ratio is 24:60 = 2:5. B's share is 5/7 × 4400 = ₹2,800 (approximately ₹3,142 - recompute: 5/7 of 4400 ≈ 3143).

Question 23Quantitative Aptitude

How many positive integers less than 500 are divisible by both 6 and 8 but not by 5?

  1. 14
  2. 16
  3. 10
  4. 12 Correct answer.

Explanation

Numbers divisible by both 6 and 8 are multiples of LCM 24. Below 500 there are ⌊499/24⌋ = 20 such multiples. Those also divisible by 5 are multiples of LCM(24,5) = 120, and there are ⌊499/120⌋ = 4 of them. Hence 20 − 4 = 16.

Question 24Quantitative Aptitude

A cone, a hemisphere and a cylinder all have the same radius and the same height equal to that radius. What is the ratio of their volumes?

  1. 1:2:6
  2. 1:3:2
  3. 2:1:3
  4. 1:2:3 Correct answer.

Explanation

With height equal to radius r, the cone volume is (1/3)πr³, the hemisphere is (2/3)πr³ and the cylinder is πr³. Multiplying by 3/πr³ gives the ratio 1:2:3.

Question 25Quantitative Aptitude

The sum of the squares of two consecutive even integers is 340. What is the larger integer?

  1. 12
  2. 18
  3. 14 Correct answer.
  4. 16

Explanation

Let the integers be n and n + 2. Then n² + (n + 2)² = 340, giving 2n² + 4n + 4 = 340, so n² + 2n − 168 = 0, which factors as (n + 14)(n − 12) = 0. Thus n = 12 and the larger integer is 14.

Question 26Quantitative Aptitude

A shopkeeper marks an article at ₹1,250 and allows a discount of 20% on the marked price. What is the selling price?

  1. ₹980
  2. ₹1,050
  3. ₹1,100
  4. ₹1,000 Correct answer.

Explanation

Discount is calculated on the marked price, so the reduction is 20% of ₹1,250 = ₹250. Selling price = 1,250 − 250 = ₹1,000. A common error is to subtract 20% of the cost instead of 20% of the marked price.

Question 27Quantitative Aptitude

The average of 6 numbers is 18. When a seventh number is included, the average becomes 20. What is the seventh number?

  1. 26
  2. 30
  3. 34
  4. 32 Correct answer.

Explanation

Sum of the first six numbers is 6 × 18 = 108. The new total must be 7 × 20 = 140. The seventh number is therefore 140 − 108 = 32.

Question 28Quantitative Aptitude

What is the value of 0.25 × 0.4 + 0.6 ÷ 0.3?

  1. 0.7
  2. 2.5
  3. 1.3
  4. 2.1 Correct answer.

Explanation

By order of operations, multiply and divide before adding. 0.25 × 0.4 = 0.1 and 0.6 ÷ 0.3 = 2, so the sum is 2.1.

Question 29Quantitative Aptitude

If x + 1/x = 3, what is the value of x² + 1/x²?

  1. 7 Correct answer.
  2. 6
  3. 11
  4. 9

Explanation

Squaring both sides gives x² + 2 + 1/x² = 9, so x² + 1/x² = 9 − 2 = 7. The middle cross term is always 2 when the product is 1.

Question 30Quantitative Aptitude

A sum becomes ₹1,300 in 2 years and ₹1,450 in 3 years at simple interest. What is the annual rate of interest?

  1. 20%
  2. 15% Correct answer.
  3. 12%
  4. 10%

Explanation

Annual simple interest equals the increase in amount per year: 1,450 − 1,300 = ₹150. The principal is 1,300 − 2(150) = ₹1,000, so rate = 150/1,000 × 100 = 15%.

Question 31Quantitative Aptitude

A bag contains 4 red and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

  1. 2/15 Correct answer.
  2. 1/5
  3. 3/10
  4. 4/25

Explanation

Probability = (4/10) × (3/9) = 12/90 = 2/15. Because the draw is without replacement, the denominator and numerator both reduce by one for the second draw.

Question 32Quantitative Aptitude

The sum of the first 20 terms of an arithmetic progression is 630, and its first term is 3. What is the common difference?

  1. 2
  2. 3 Correct answer.
  3. 4
  4. 1.5

Explanation

Using S = (n/2)[2a + (n−1)d]: 630 = 10[6 + 19d], so 63 = 6 + 19d and d = 3.

Question 33Quantitative Aptitude

A rectangular field is 40 m by 30 m. A path of uniform width 2 m runs inside along its boundary. What is the area of the path?

  1. 264 m² Correct answer.
  2. 300 m²
  3. 256 m²
  4. 240 m²

Explanation

Outer area = 40 × 30 = 1,200 m². The inner rectangle is 36 × 26 = 936 m². Path area = 1,200 − 936 = 264 m².

Question 34Quantitative Aptitude

If a : b = 2 : 3 and b : c = 4 : 5, what is a : c?

  1. 5 : 8
  2. 8 : 15 Correct answer.
  3. 3 : 4
  4. 2 : 5

Explanation

Make b common by using the LCM of 3 and 4, which is 12. Then a : b = 8 : 12 and b : c = 12 : 15, giving a : c = 8 : 15.

Question 35Quantitative Aptitude

A shopkeeper sells an article at a loss of 10%. Had he sold it for ₹60 more, he would have gained 5%. What is the cost price?

  1. ₹600
  2. ₹400 Correct answer.
  3. ₹450
  4. ₹300

Explanation

The gap between a 10% loss and a 5% gain is 15% of the cost price. So 15% of CP = ₹60, giving CP = 60/0.15 = ₹400.

Question 36Quantitative Aptitude

The LCM of two numbers is 495 and their HCF is 5. If their sum is 100, what is their difference?

  1. 15
  2. 20
  3. 10 Correct answer.
  4. 5

Explanation

Product of the numbers = HCF × LCM = 5 × 495 = 2,475. With sum 100, the numbers are 55 and 45, whose product is 2,475. Their difference is 10.

Question 37Quantitative Aptitude

A man rows at 6 km/h in still water. The river flows at 2 km/h. What is the total time to go 16 km downstream and return 16 km upstream?

  1. 5 hours
  2. 8 hours
  3. 7 hours
  4. 6 hours Correct answer.

Explanation

Downstream speed = 8 km/h and upstream speed = 4 km/h. Time = 16/8 + 16/4 = 2 + 4 = 6 hours.

Question 38Quantitative Aptitude

The volume of a sphere is 36π cm³. What is its surface area?

  1. 36π cm² Correct answer.
  2. 9π cm²
  3. 18π cm²
  4. 72π cm²

Explanation

From (4/3)πr³ = 36π, r³ = 27, so r = 3. Surface area = 4πr² = 4π(9) = 36π cm².

Question 39Quantitative Aptitude

If 2^(x+1) = 8^(x−1), what is the value of x?

  1. 3
  2. 4
  3. 1
  4. 2 Correct answer.

Explanation

Write 8 as 2³, so 8^(x−1) = 2^(3x−3). Equating exponents: x + 1 = 3x − 3, giving 2x = 4 and x = 2.

Question 40Quantitative Aptitude

In how many ways can the letters of the word 'LEVEL' be arranged?

  1. 120
  2. 60
  3. 30 Correct answer.
  4. 20

Explanation

The word has 5 letters with L repeated twice and E repeated twice. Arrangements = 5!/(2! × 2!) = 120/4 = 30.

Question 41Quantitative Aptitude

A cone has base radius 7 cm and height 24 cm. What is its slant height?

  1. 26 cm
  2. 23 cm
  3. 25 cm Correct answer.
  4. 31 cm

Explanation

Slant height l = √(r² + h²) = √(49 + 576) = √625 = 25 cm. The radius, height and slant height form a right triangle.

Question 42Quantitative Aptitude

The average age of a class of 30 students is 15 years. When the teacher's age is included, the average rises by 1 year. What is the teacher's age?

  1. 45 years
  2. 46 years Correct answer.
  3. 50 years
  4. 44 years

Explanation

Students' total = 30 × 15 = 450. New total for 31 people = 31 × 16 = 496. Teacher's age = 496 − 450 = 46 years.

Question 43Quantitative Aptitude

Two dice are thrown together. What is the probability that the sum of the numbers is a prime number?

  1. 1/2
  2. 5/12 Correct answer.
  3. 7/18
  4. 1/3

Explanation

Prime sums possible are 2, 3, 5, 7, 11, with counts 1, 2, 4, 6, 2 = 15 outcomes. Probability = 15/36 = 5/12.

Question 44Quantitative Aptitude

A and B together can do a job in 12 days, B and C in 15 days, and A and C in 20 days. In how many days can A alone do the job?

  1. 30 Correct answer.
  2. 24
  3. 40
  4. 20

Explanation

Add all three rates: 2(A + B + C) = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. So A + B + C = 1/10 per day. A alone = 1/10 − 1/15 = 1/30, giving 30 days.

Question 45Quantitative Aptitude

How many three-digit numbers are divisible by 7 but not by 14?

  1. 64
  2. 128
  3. 65 Correct answer.
  4. 63

Explanation

Three-digit multiples of 7 run from 105 to 994, giving (994 − 105)/7 + 1 = 128. Multiples of 14 are the even ones, numbering 64. So 128 − 64 = 65 are divisible by 7 but not by 14.

Question 46Quantitative Aptitude

A sum of money invested at compound interest, compounded annually, amounts to ₹13,310 in 3 years and ₹12,100 in 2 years. What is the rate of interest per annum?

  1. 12%
  2. 8%
  3. 15%
  4. 10% Correct answer.

Explanation

The amount grows by a factor of 13,310/12,100 = 1.1 in one year, so the rate is 10%. Compound interest fixes the growth factor per year regardless of the base amount.

Question 47Quantitative Aptitude

In a mixture of 60 litres, milk and water are in the ratio 7 : 3. How much water must be added so that the ratio becomes 3 : 2?

  1. 12 litres
  2. 8 litres Correct answer.
  3. 6 litres
  4. 10 litres

Explanation

Milk = 42 L and water = 18 L. For milk : water = 3 : 2, water needed = 42 × 2/3 = 28 L. Extra water = 28 − 18 = 8 litres.

Question 48Quantitative Aptitude

A cylindrical vessel of radius 7 cm contains water to a height of 10 cm. A solid sphere of radius 3.5 cm is fully immersed. By how much does the water level rise?

  1. 7/3 cm
  2. 2 cm
  3. 1 cm
  4. 7/6 cm Correct answer.

Explanation

Sphere volume = (4/3)π(3.5)³ = (4/3)π(42.875) = 171.5π/3 cm³. Rise = volume ÷ (π × 7²) = (171.5/3)/49 = 3.5/3 = 7/6 cm.

Question 49Quantitative Aptitude

If the roots of the equation x² − px + 36 = 0 are equal, and p is positive, what is the value of p?

  1. 36
  2. 12 Correct answer.
  3. 6
  4. 18

Explanation

Equal roots require the discriminant to vanish: p² − 4(1)(36) = 0, so p² = 144 and p = 12 (positive).

Question 50Quantitative Aptitude

A trader marks an article 40% above its cost price and then allows a discount of 25% on the marked price. What is the profit or loss percentage?

  1. 15% profit
  2. 5% loss
  3. 10% profit
  4. 5% profit Correct answer.

Explanation

Take cost price as 100. Marked price becomes 140, and a 25% discount reduces it by 35, giving a selling price of 105. Profit is 5 on a cost of 100, so the profit percentage is 5%.