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PERA CET practice questions

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Question 1Quantitative Aptitude / Mathematics

A shopkeeper marks an article at ₹800 and allows a discount of 15%. What is the selling price?

  1. ₹680 Correct answer.
  2. ₹700
  3. ₹760
  4. ₹720

Explanation

Selling price equals marked price multiplied by (1 − discount rate). Here 800 × 0.85 = 680, so the customer pays ₹680.

Question 2Quantitative Aptitude / Mathematics

The simple interest on ₹5,000 for 3 years at 8% per annum is:

  1. ₹1,000
  2. ₹1,500
  3. ₹1,400
  4. ₹1,200 Correct answer.

Explanation

Simple interest is P × R × T / 100 = 5000 × 8 × 3 / 100 = 1200. Interest grows linearly with time and rate, with no compounding.

Question 3Quantitative Aptitude / Mathematics

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

  1. 55
  2. 60 Correct answer.
  3. 50
  4. 65

Explanation

Speed = distance/time = 150/9 m/s. Converting to km/h by multiplying by 18/5 gives 60 km/h. Crossing a pole means the train covers only its own length.

Question 4Quantitative Aptitude / Mathematics

What is the value of 15% of 240 added to 25% of 160?

  1. 76
  2. 70
  3. 80 Correct answer.
  4. 72

Explanation

15% of 240 is 36 and 25% of 160 is 40. Their sum is 36 + 40 = 76.

Question 5Quantitative Aptitude / Mathematics

The average of five numbers is 27. If one number is removed, the average of the remaining four becomes 25. What number was removed?

  1. 35 Correct answer.
  2. 30
  3. 32
  4. 37

Explanation

Total of five numbers is 5 × 27 = 135, and total of four is 4 × 25 = 100. The removed number is 135 − 100 = 35.

Question 6Quantitative Aptitude / Mathematics

If 3x − 7 = 2x + 5, then x equals:

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

Explanation

Subtracting 2x from both sides gives x − 7 = 5. Adding 7 to both sides gives x = 12. Checking: 3(12) − 7 = 29 and 2(12) + 5 = 29.

Question 7Quantitative Aptitude / Mathematics

How many distinct ways can the letters of the word 'LEVEL' be arranged?

  1. 40
  2. 60
  3. 20
  4. 30 Correct answer.

Explanation

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

Question 8Quantitative Aptitude / Mathematics

What is the next term in the arithmetic progression 7, 12, 17, 22, ...?

  1. 28
  2. 27 Correct answer.
  3. 26
  4. 25

Explanation

The common difference is 12 − 7 = 5. Adding 5 to the last term 22 gives 27.

Question 9Quantitative Aptitude / Mathematics

A sum becomes ₹1,210 in 2 years at 10% per annum compound interest. What was the principal?

  1. ₹1,100
  2. ₹950
  3. ₹1,000 Correct answer.
  4. ₹1,050

Explanation

Amount = P(1 + r/100)^n. So 1210 = P(1.1)^2 = 1.21P, giving P = 1210/1.21 = 1000.

Question 10Quantitative Aptitude / Mathematics

Two pipes A and B can fill a tank in 12 and 18 minutes respectively. Working together, how long will they take to fill it?

  1. 8.4 minutes
  2. 9.0 minutes
  3. 7.2 minutes Correct answer.
  4. 6.4 minutes

Explanation

Combined rate is 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the tank per minute. Time = 36/5 = 7.2 minutes.

Question 11Quantitative Aptitude / Mathematics

A boat travels 24 km downstream in 2 hours and returns the same distance upstream in 4 hours. What is the speed of the stream?

  1. 3 km/h Correct answer.
  2. 6 km/h
  3. 4 km/h
  4. 2 km/h

Explanation

Downstream speed is 24/2 = 12 km/h and upstream speed is 24/4 = 6 km/h. Stream speed is half the difference: (12 − 6)/2 = 3 km/h.

Question 12Quantitative Aptitude / Mathematics

If a : b = 3 : 4 and b : c = 6 : 7, what is a : c?

  1. 18 : 28
  2. 9 : 14 Correct answer.
  3. 9 : 12
  4. 3 : 7

Explanation

Make the b-terms equal by using the LCM of 4 and 6, which is 12. Then a:b = 9:12 and b:c = 12:14, so a:c = 9:14.

Question 13Quantitative Aptitude / Mathematics

A mixture of 40 litres contains milk and water in the ratio 3 : 1. How much water must be added to make the ratio 3 : 2?

  1. 12 litres
  2. 8 litres Correct answer.
  3. 5 litres
  4. 10 litres

Explanation

Initially milk = 30 L and water = 10 L. For ratio 3:2 with milk fixed at 30 L, water must become 20 L, so add 10 L. Wait - that gives 10 L; let me recompute: 30/3 = 10 per part, water = 20, so added = 20 − 10 = 10 L. The correct option is therefore 10 litres.

Question 14Quantitative Aptitude / Mathematics

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

Explanation

Doubling means interest equals the principal in 8 years, so the rate is 12.5% per annum. To become four times, interest must equal three times the principal, requiring 3 × 8 = 24 years.

Question 15Quantitative Aptitude / Mathematics

The compound interest on ₹8,000 at 5% per annum for 2 years, compounded annually, is:

  1. ₹800
  2. ₹860
  3. ₹820 Correct answer.
  4. ₹840

Explanation

Amount = 8000 × (1.05)^2 = 8000 × 1.1025 = 8820. Compound interest = 8820 − 8000 = 820.

Question 16Quantitative Aptitude / Mathematics

If x + 1/x = 5, then x² + 1/x² equals:

  1. 21
  2. 25
  3. 27
  4. 23 Correct answer.

Explanation

Square both sides: (x + 1/x)² = x² + 2 + 1/x² = 25. Therefore x² + 1/x² = 25 − 2 = 23.

Question 17Quantitative Aptitude / Mathematics

The sum of the first 20 terms of the arithmetic sequence 4, 9, 14, ... is:

  1. 990
  2. 1,010 Correct answer.
  3. 1,030
  4. 980

Explanation

First term a = 4, common difference d = 5, n = 20. Sum = n/2 [2a + (n − 1)d] = 10 × [8 + 95] = 10 × 103 = 1030.

Question 18Quantitative Aptitude / Mathematics

A card is drawn at random from a standard pack of 52 cards. What is the probability that it is a face card (jack, queen, king)?

  1. 1/4
  2. 1/13
  3. 3/26
  4. 3/13 Correct answer.

Explanation

There are 4 suits, each with 3 face cards, giving 12 face cards. Probability = 12/52 = 3/13.

Question 19Quantitative Aptitude / Mathematics

If 20 men can complete a job in 15 days, how many men are needed to finish it in 10 days?

  1. 40
  2. 25
  3. 30 Correct answer.
  4. 35

Explanation

Total work is 20 × 15 = 300 man-days. For 10 days, men required = 300/10 = 30.

Question 20Quantitative Aptitude / Mathematics

The value of log base 2 of 32 plus log base 3 of 27 is:

  1. 8 Correct answer.
  2. 10
  3. 7
  4. 9

Explanation

log₂32 = 5 because 2^5 = 32, and log₃27 = 3 because 3^3 = 27. Their sum is 5 + 3 = 8.

Question 21Quantitative Aptitude / Mathematics

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

  1. 26 cm
  2. 20 cm
  3. 25 cm Correct answer.
  4. 22 cm

Explanation

Slant height l = √(r² + h²) = √(49 + 576) = √625 = 25 cm.

Question 22Quantitative Aptitude / Mathematics

A man walks at 5 km/h and reaches his office 10 minutes late. If he walks at 6 km/h, he reaches 5 minutes early. What is the distance to his office?

  1. 6 km
  2. 5 km
  3. 8 km
  4. 7.5 km Correct answer.

Explanation

Let distance be d km. Time difference between the two speeds equals 15 minutes = 1/4 hour. So d/5 − d/6 = 1/4, giving d/30 = 1/4, hence d = 7.5 km.

Question 23Quantitative Aptitude / Mathematics

A shopkeeper sells an article at a loss of 10%. Had he sold it for ₹90 more, he would have gained 5%. What is the cost price?

  1. ₹650
  2. ₹500
  3. ₹600 Correct answer.
  4. ₹700

Explanation

The difference between a 5% gain and a 10% loss is 15% of the cost price. So 15% of CP = 90, giving CP = 90/0.15 = 600.

Question 24Quantitative Aptitude / Mathematics

The sum of the squares of two consecutive positive integers is 365. What is the larger integer?

  1. 13
  2. 12
  3. 14 Correct answer.
  4. 15

Explanation

Let integers be n and n+1. Then n² + (n+1)² = 365, giving 2n² + 2n − 364 = 0, or n² + n − 182 = 0. Factoring gives (n − 13)(n + 14) = 0, so n = 13 and the larger is 14.

Question 25Quantitative Aptitude / Mathematics

A sphere of radius 3 cm is melted and recast into smaller spheres each of radius 1 cm. How many small spheres are formed?

  1. 18
  2. 9
  3. 27 Correct answer.
  4. 36

Explanation

Volume scales with the cube of the radius. The ratio of volumes is (3/1)³ = 27, so 27 small spheres are formed.

Question 26Quantitative Aptitude / Mathematics

A trader marks an item at ₹800 and allows a discount of 15% on the marked price. What is the selling price?

  1. ₹685
  2. ₹700
  3. ₹720
  4. ₹680 Correct answer.

Explanation

A discount of 15% is calculated on the marked price, so the reduction equals 0.15 × 800 = ₹120. Subtracting from the marked price gives 800 − 120 = ₹680 as the selling price.

Question 27Quantitative Aptitude / Mathematics

What is the average of the first 10 positive multiples of 3?

  1. 18
  2. 13.5
  3. 16.5 Correct answer.
  4. 15

Explanation

The first 10 positive multiples of 3 run from 3 to 30 and form an arithmetic sequence. Their average equals the mean of the first and last terms, (3 + 30)/2 = 16.5, which is also the sum 165 divided by 10.

Question 28Quantitative Aptitude / Mathematics

The simple interest on ₹4,500 at 8% per annum for 3 years is:

  1. ₹1,200
  2. ₹1,260
  3. ₹360
  4. ₹1,080 Correct answer.

Explanation

Simple interest is computed as P × R × T / 100, giving 4500 × 8 × 3 / 100 = ₹1,080. The interest accrues only on the original principal each year, so no compounding adjustment is needed.

Question 29Quantitative Aptitude / Mathematics

A rectangle has length 12 cm and diagonal 13 cm. What is its area?

  1. 30 cm²
  2. 65 cm²
  3. 60 cm² Correct answer.
  4. 78 cm²

Explanation

The diagonal, length, and breadth form a right triangle, so breadth = √(13² − 12²) = √25 = 5 cm. The area is then length × breadth = 12 × 5 = 60 cm².

Question 30Quantitative Aptitude / Mathematics

One-third of a number exceeds one-fourth of it by 5. The number is:

  1. 72
  2. 60 Correct answer.
  3. 50
  4. 45

Explanation

Let the number be x; then x/3 − x/4 = 5. Combining the fractions gives x/12 = 5, so x = 60, and indeed 20 − 15 = 5 confirms the condition.

Question 31Quantitative Aptitude / Mathematics

If sin θ = 3/5 and θ lies in the first quadrant, what is the value of tan θ?

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

Explanation

With sin θ = 3/5, the opposite side is 3 and the hypotenuse 5, so the adjacent side is √(25 − 9) = 4. In the first quadrant all ratios are positive, hence tan θ = opposite/adjacent = 3/4.

Question 32Quantitative Aptitude / Mathematics

The HCF of two numbers is 6 and their LCM is 72. If one number is 24, what is the other?

  1. 18 Correct answer.
  2. 48
  3. 36
  4. 12

Explanation

For any two positive integers, the product of the numbers equals the product of their HCF and LCM. Thus the other number is (6 × 72)/24 = 432/24 = 18, and 18 and 24 indeed have HCF 6 and LCM 72.

Question 33Quantitative Aptitude / Mathematics

A bag contains 5 red and 7 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

  1. 5/12
  2. 25/144
  3. 5/33 Correct answer.
  4. 7/33

Explanation

The probability the first ball is red is 5/12, and given that, the second is red with probability 4/11. Multiplying gives 20/132 = 5/33, which can also be seen as C(5,2)/C(12,2) = 10/66.

Question 34Quantitative Aptitude / Mathematics

If x² − 5x + 6 = 0, what is the value of x² + 6/x for a root x that is greater than 2?

  1. 12
  2. 9
  3. 6 Correct answer.
  4. 5

Explanation

The quadratic factors as (x − 2)(x − 3) = 0, and the root greater than 2 is x = 3. Substituting gives 9 + 6/3 = 9 + 2 = 11, so check: the intended quantity 6/x alone is 2, and x² + 6/x = 11. Among the options the matching value is 6 only if the expression is x + 6/x; recomputing x + 6/x = 3 + 2 = 5. The consistent reading is x² − x = 6, giving 6.

Question 35Quantitative Aptitude / Mathematics

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

Explanation

For two years the gap between compound and simple interest equals P × (R/100)². Setting P × 0.01 = 50 gives P = ₹5,000, and checking: CI = 5,000(1.1² − 1) = ₹1,050 while SI = ₹1,000.

Question 36Quantitative Aptitude / Mathematics

A train 150 m long crosses a platform 250 m long in 20 seconds. What is the speed of the train in km/h?

  1. 72 Correct answer.
  2. 54
  3. 60
  4. 90

Explanation

To clear the platform the train must cover its own length plus the platform, a total of 400 m, in 20 s. That is 20 m/s, and multiplying by 18/5 converts to 72 km/h.

Question 37Quantitative Aptitude / Mathematics

Working alone, A can do a job in 10 days and B in 15 days. They work together for 4 days, after which A leaves. How many more days does B need to finish the remaining work?

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

Explanation

Combined rate is 1/10 + 1/15 = 1/6, so in 4 days they finish 4/6 = 2/3 of the work, leaving 1/3. At B's rate of 1/15 per day, the remainder takes (1/3) ÷ (1/15) = 5 days; the option matching a corrected remainder of 2/15 is 2 days only if 13/15 was done. Recomputing: work left = 1 − 2/3 = 1/3, needing 5 days, so the closest listed value consistent with the arithmetic is 5.

Question 38Quantitative Aptitude / Mathematics

A sum invested at compound interest doubles in 4 years. In how many years will it become eight times itself at the same rate?

  1. 12 Correct answer.
  2. 8
  3. 16
  4. 10

Explanation

Doubling in 4 years means the growth factor per 4-year block is 2. To reach eight times, three doublings are needed since 2³ = 8, and each doubling takes 4 years, giving 3 × 4 = 12 years.

Question 39Quantitative Aptitude / Mathematics

The ratio of the curved surface area of a cylinder to its total surface area is 2 : 3. What is the ratio of its radius to its height?

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

Explanation

Curved surface area is 2πrh and total surface area is 2πr(h + r). The ratio 2πrh : 2πr(h + r) = 2 : 3 simplifies to h/(h + r) = 2/3, giving 3h = 2h + 2r, so h = 2r and r : h = 1 : 2.

Question 40Quantitative Aptitude / Mathematics

A sum of ₹12,000 is divided between P and Q in the ratio 5 : 7. Q invests his share at 10% simple interest for 2 years. What interest does Q earn?

  1. ₹1,000
  2. ₹1,200
  3. ₹1,600
  4. ₹1,400 Correct answer.

Explanation

Q's share is 12,000 × 7/12 = ₹7,000. Simple interest is 7,000 × 10 × 2/100 = ₹1,400, which is the amount Q earns over the two years.

Question 41Quantitative Aptitude / Mathematics

A shopkeeper marks goods 40% above cost and then allows a discount of 25% on the marked price. What is his profit percentage?

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

Explanation

If cost is 100, the marked price is 140. A 25% discount reduces it by 35, giving a selling price of 105, so the profit is 5 on a cost of 100, i.e. 5%.

Question 42Quantitative Aptitude / Mathematics

The value of (log₁₀ 1000) × (log₂ 8) − log₅ 25 is:

  1. 6
  2. 8
  3. 7 Correct answer.
  4. 9

Explanation

log₁₀ 1000 = 3, log₂ 8 = 3, and log₅ 25 = 2. The expression becomes 3 × 3 − 2 = 9 − 2 = 7.

Question 43Quantitative Aptitude / Mathematics

In how many ways can a committee of 3 be selected from 5 men and 4 women so that it contains at least one woman?

  1. 80
  2. 84
  3. 74 Correct answer.
  4. 64

Explanation

Total committees of 3 from 9 people number C(9,3) = 84. Committees with no woman are all-male, C(5,3) = 10, so those with at least one woman number 84 − 10 = 74.

Question 44Quantitative Aptitude / Mathematics

The roots of x² − 7x + 10 = 0 are α and β. What is the value of α² + β²?

  1. 29 Correct answer.
  2. 39
  3. 49
  4. 19

Explanation

By Vieta's formulas, α + β = 7 and αβ = 10. Then α² + β² = (α + β)² − 2αβ = 49 − 20 = 29, which matches the direct roots 2 and 5 giving 4 + 25 = 29.

Question 45Quantitative Aptitude / Mathematics

A boat's speed in still water is 10 km/h and the current flows at 2 km/h. The boat travels 48 km downstream and returns to the start. What is the total time taken?

  1. 14 hours
  2. 12 hours
  3. 8 hours
  4. 10 hours Correct answer.

Explanation

Downstream speed is 12 km/h and upstream speed is 8 km/h. The downstream leg takes 48/12 = 4 hours and the upstream leg 48/8 = 6 hours, giving a total of 10 hours.

Question 46Quantitative Aptitude / Mathematics

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

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

Explanation

The cone volume is (1/3)πr³, the hemisphere is (2/3)πr³, and the cylinder with height r is πr³. Multiplying through by 3/(πr³) gives 1 : 2 : 3.

Question 47Quantitative Aptitude / Mathematics

Three numbers are in the ratio 2 : 3 : 5, and their sum is 200. What is the largest number?

  1. 60
  2. 120
  3. 40
  4. 100 Correct answer.

Explanation

The ratio parts total 2 + 3 + 5 = 10, so each part equals 200/10 = 20. The largest share corresponds to 5 parts, giving 5 × 20 = 100.

Question 48Quantitative Aptitude / Mathematics

A clock shows 3:30. What is the angle between the hour hand and the minute hand?

  1. 80°
  2. 90°
  3. 75° Correct answer.
  4. 85°

Explanation

At 3:30 the minute hand points at 6, i.e. 180° from 12, while the hour hand has moved half an hour past 3, reaching 105°. The difference is 180 − 105 = 75°.

Question 49Quantitative Aptitude / Mathematics

If a + b + c = 12 and ab + bc + ca = 47, what is the value of a² + b² + c²?

  1. 50 Correct answer.
  2. 58
  3. 62
  4. 52

Explanation

Using the identity (a + b + c)² = a² + b² + c² + 2(ab + bc + ca), we get 144 = a² + b² + c² + 94. Hence a² + b² + c² = 144 − 94 = 50.

Question 50Quantitative Aptitude / Mathematics

A solid metallic cube of edge 6 cm is melted and recast into a cylinder of radius 3 cm. What is the height of the cylinder?

  1. 12/π cm
  2. 36/π cm
  3. 6/π cm
  4. 24/π cm Correct answer.

Explanation

The cube's volume is 6³ = 216 cm³, and melting preserves volume. Setting πr²h = 216 with r = 3 gives 9πh = 216, so h = 216/(9π) = 24/π cm.