PET Practice Set 21

UPSSSC PET (Preliminary Eligibility Test) · 2026 · with answers and explanations

questions
37
Total marks
37
Duration
120 minutes
Negative marking
−0.25

Subjects: Mathematics

Question 1

Mathematics · 1 marks · −0.25

In how many years will a sum of money double itself at 12.5% per annum simple interest?

  1. A.6 years
  2. B.8 years
  3. C.10 years
  4. D.12 years

Correct answer: B

Explanation: For doubling, SI = P. So P = (P × 12.5 × T)/100. T = 100/12.5 = 8 years.

Question 2

Mathematics · 1 marks · −0.25

The difference between compound interest and simple interest on Rs. 10,000 at 10% per annum for 2 years is:

  1. A.Rs. 100
  2. B.Rs. 120
  3. C.Rs. 150
  4. D.Rs. 200

Correct answer: A

Explanation: CI − SI for 2 years = P × (R/100)^2 = 10000 × (10/100)^2 = 10000 × 0.01 = Rs. 100.

Question 3

Mathematics · 1 marks · −0.25

A sum of Rs. 12,000 at compound interest becomes double after 5 years. How much will it be after 20 years?

  1. A.Rs. 1,20,000
  2. B.Rs. 1,44,000
  3. C.Rs. 1,92,000
  4. D.Rs. 1,50,000

Correct answer: C

Explanation: Doubles every 5 years. After 20 years = 4 doubling periods. 12000 × 2^4 = 12000 × 16 = Rs. 1,92,000.

Question 4

Mathematics · 1 marks · −0.25

What sum will earn a simple interest of Rs. 4800 in 4 years at the rate of 12% per annum?

  1. A.Rs. 10,000
  2. B.Rs. 12,000
  3. C.Rs. 8,000
  4. D.Rs. 15,000

Correct answer: A

Explanation: P = (SI × 100)/(R × T) = (4800 × 100)/(12 × 4) = 480000/48 = Rs. 10,000.

Question 5

Mathematics · 1 marks · −0.25

A sum becomes Rs. 8,820 after 2 years and Rs. 9,261 after 3 years under compound interest. Find the rate.

  1. A.5%
  2. B.6%
  3. C.4%
  4. D.8%

Correct answer: A

Explanation: Interest for the 3rd year = 9261 − 8820 = 441. Rate = (441/8820) × 100 = 5%.

Question 6

Mathematics · 1 marks · −0.25

A sum doubles itself in 5 years at compound interest. In how many years will it become 8 times?

  1. A.15
  2. B.10
  3. C.20
  4. D.12

Correct answer: A

Explanation: 8 = 2^3. If it doubles in 5 years, it becomes 2^3 = 8 times in 3 × 5 = 15 years.

Question 7

Mathematics · 1 marks · −0.25

A person borrowed Rs. 4000 for 2 years at simple interest and paid Rs. 480 as interest. What is the rate of interest?

  1. A.5%
  2. B.6%
  3. C.7%
  4. D.8%

Correct answer: B

Explanation: R = (SI × 100)/(P × T) = (480 × 100)/(4000 × 2) = 48000/8000 = 6%.

Question 8

Mathematics · 1 marks · −0.25

Average of three numbers is 40. If the average of two of them is 38, find the third number.

  1. A.38
  2. B.40
  3. C.42
  4. D.44

Correct answer: D

Explanation: Sum of three = 40 × 3 = 120. Sum of two = 38 × 2 = 76. Third number = 120 − 76 = 44.

Question 9

Mathematics · 1 marks · −0.25

The average of 99 numbers is 27. If 3 is added to each number, the new average is:

  1. A.3
  2. B.30
  3. C.10
  4. D.27

Correct answer: B

Explanation: When a constant is added to each number, the average increases by that constant. New average = 27 + 3 = 30.

Question 10

Mathematics · 1 marks · −0.25

The average of 13 results is 68. The average of the first 7 is 63 and the average of the last 7 is 70. Find the 7th result.

  1. A.47
  2. B.65.5
  3. C.73.5
  4. D.94

Correct answer: A

Explanation: Total = 68 × 13 = 884. First 7 sum = 63 × 7 = 441. Last 7 sum = 70 × 7 = 490. 7th result = 441 + 490 − 884 = 47.

Question 11

Mathematics · 1 marks · −0.25

The average age of 20 teachers is 50 years. When a 40-year-old teacher leaves and a new teacher joins, the average increases by 1 year. The new teacher's age is:

  1. A.50
  2. B.55
  3. C.60
  4. D.65

Correct answer: C

Explanation: Original total = 20 × 50 = 1000. New total = 21 × 51 = 1020... Actually with same count: new total = 20 × 51 = 1020. New teacher's age = 1020 − (1000 − 40) = 1020 − 960 = 60.

Question 12

Mathematics · 1 marks · −0.25

A cricket team captain is 28 years old and the wicket keeper is 4 years older. If the average of the remaining 9 players is 2 years less than the whole team's average, the team average is:

  1. A.15 years
  2. B.22 years
  3. C.21 years
  4. D.29 years

Correct answer: C

Explanation: Let team average = x. Sum = 11x. Captain = 28, WK = 32, total = 60. Remaining 9 average = x − 2. So 9(x − 2) = 11x − 60. 9x − 18 = 11x − 60. 2x = 42. x = 21.

Question 13

Mathematics · 1 marks · −0.25

What is the average of the first seven prime numbers?

  1. A.7.14
  2. B.8.76
  3. C.7.64
  4. D.8.29

Correct answer: D

Explanation: First seven primes: 2, 3, 5, 7, 11, 13, 17. Sum = 58. Average = 58/7 ≈ 8.29.

Question 14

Mathematics · 1 marks · −0.25

If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?

  1. A.60
  2. B.45
  3. C.40
  4. D.30

Correct answer: A

Explanation: (A+B)'s one day work = 1/15. B's one day work = 1/20. A's one day work = 1/15 − 1/20 = (4−3)/60 = 1/60. A alone takes 60 days.

Question 15

Mathematics · 1 marks · −0.25

A and B together can complete a work in 3 days. They start together but after 2 days B leaves. If the remaining work is completed in 2 more days, B alone could do the work in:

  1. A.5 days
  2. B.6 days
  3. C.9 days
  4. D.10 days

Correct answer: B

Explanation: (A+B) do 1/3 per day. In 2 days = 2/3 done. Remaining 1/3 done by A in 2 days, so A = 1/6 per day. B = 1/3 − 1/6 = 1/6 per day. B alone = 6 days.

Question 16

Mathematics · 1 marks · −0.25

A can complete work in 18 days, B in 20 days, C in 30 days. B and C start and leave after 2 days. Time for A to complete the remaining work:

  1. A.10 days
  2. B.12 days
  3. C.15 days
  4. D.16 days

Correct answer: C

Explanation: (B+C) per day = 1/20 + 1/30 = 5/60 = 1/12. In 2 days = 1/6. Remaining = 5/6. A per day = 1/18. Time = (5/6)/(1/18) = 15 days.

Question 17

Mathematics · 1 marks · −0.25

Working 5 hours a day, A can complete work in 8 days. Working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they jointly complete the work in:

  1. A.3 days
  2. B.4 days
  3. C.4.5 days
  4. D.5.4 days

Correct answer: A

Explanation: A needs 40 man-hours, B needs 60 man-hours. Combined hourly rate = 1/40 + 1/60 = 5/120 = 1/24. At 8 hours/day: 24/8 = 3 days.

Question 18

Mathematics · 1 marks · −0.25

If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same work is:

  1. A.12 days
  2. B.10 days
  3. C.9 days
  4. D.8 days

Correct answer: B

Explanation: Total work = 10 × 12 = 120 man-days. Time for 12 men = 120/12 = 10 days.

Question 19

Mathematics · 1 marks · −0.25

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, B alone takes:

  1. A.30 days
  2. B.35 days
  3. C.40 days
  4. D.45 days

Correct answer: A

Explanation: Let B = x days, A = 1.5x days. Together: 1/x + 1/(1.5x) = 1/18. (1 + 2/3)/x = 1/18. (5/3)/x = 1/18. x = 5 × 18/3 = 30 days.

Question 20

Mathematics · 1 marks · −0.25

A man walking at 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is:

  1. A.600
  2. B.750
  3. C.1000
  4. D.1250

Correct answer: D

Explanation: Speed = 5 km/hr = 5000/60 m/min = 250/3 m/min. Distance = (250/3) × 15 = 1250 m.

Question 21

Mathematics · 1 marks · −0.25

A 300 m long train running at 25 m/sec crosses a 200 m long bridge in:

  1. A.5 seconds
  2. B.10 seconds
  3. C.20 seconds
  4. D.25 seconds

Correct answer: C

Explanation: Total distance = 300 + 200 = 500 m. Time = 500/25 = 20 seconds.

Question 22

Mathematics · 1 marks · −0.25

A car covers a distance at 60 km/hr in 1 hour. Time for another car at 40 km/hr to cover the same distance:

  1. A.5/2 hours
  2. B.2 hours
  3. C.3/2 hours
  4. D.1 hour

Correct answer: C

Explanation: Distance = 60 km. Time = 60/40 = 3/2 hours = 1.5 hours.

Question 23

Mathematics · 1 marks · −0.25

A man travels from city A to city B at 40 km/hr and returns at 60 km/hr. His average speed for the round trip is:

  1. A.48 km/hr
  2. B.50 km/hr
  3. C.54 km/hr
  4. D.55 km/hr

Correct answer: A

Explanation: Average speed for equal distances = 2 × 40 × 60 / (40 + 60) = 4800/100 = 48 km/hr.

Question 24

Mathematics · 1 marks · −0.25

Walking at 3/4 of his usual speed, a man reaches office 20 minutes late. His usual time is:

  1. A.75 minutes
  2. B.60 minutes
  3. C.40 minutes
  4. D.30 minutes

Correct answer: B

Explanation: At 3/4 speed, time = 4/3 of usual. Extra time = 4/3T − T = T/3 = 20. So T = 60 minutes.

Question 25

Mathematics · 1 marks · −0.25

A train running at 84 km/hr passes a man walking in the opposite direction at 6 km/hr in 4 seconds. The length of the train is:

  1. A.150 m
  2. B.120 m
  3. C.100 m
  4. D.90 m

Correct answer: C

Explanation: Relative speed = 84 + 6 = 90 km/hr = 90 × 5/18 = 25 m/sec. Length = 25 × 4 = 100 m.

Question 26

Mathematics · 1 marks · −0.25

The ratio between the length and breadth of a rectangular park is 3:2. If a man cycling at 12 km/hr completes one round in 8 minutes, the area of the park is:

  1. A.15,360 sq m
  2. B.153,600 sq m
  3. C.30,720 sq m
  4. D.307,200 sq m

Correct answer: B

Explanation: Perimeter = 12000/60 × 8 = 1600 m. With L:B = 3:2, 2(3x + 2x) = 1600, 10x = 1600, x = 160. L = 480, B = 320. Area = 480 × 320 = 153,600 sq m.

Question 27

Mathematics · 1 marks · −0.25

If each side of a rectangle is increased by 20%, the percentage increase in area is:

  1. A.40%
  2. B.42%
  3. C.44%
  4. D.46%

Correct answer: C

Explanation: New area = 1.2L × 1.2B = 1.44LB. Increase = 44%.

Question 28

Mathematics · 1 marks · −0.25

A rectangular tank is 15 m 17 cm long and 9 m 2 cm broad. The minimum number of square tiles needed to pave its floor is:

  1. A.814
  2. B.820
  3. C.840
  4. D.844

Correct answer: A

Explanation: HCF(1517 cm, 902 cm) = 41 cm. Tiles = (1517 × 902)/(41 × 41) = (37 × 22) = 814.

Question 29

Mathematics · 1 marks · −0.25

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the 3 cm side to form a cone. The volume of the cone is:

  1. A.12π cu cm
  2. B.15π cu cm
  3. C.16π cu cm
  4. D.20π cu cm

Correct answer: A

Explanation: Radius = 3 cm, height = 4 cm. Volume = (1/3)πr²h = (1/3) × π × 9 × 4 = 12π cu cm.

Question 30

Mathematics · 1 marks · −0.25

After bleaching, a towel loses 20% of its length and 10% of its breadth. The percentage decrease in area is:

  1. A.10%
  2. B.10.08%
  3. C.20%
  4. D.28%

Correct answer: D

Explanation: New area = 0.8L × 0.9B = 0.72LB. Decrease = 28%.

Question 31

Mathematics · 1 marks · −0.25

A rectangle has diagonal √41 cm and area 20 sq cm. Its perimeter is:

  1. A.9 cm
  2. B.18 cm
  3. C.20 cm
  4. D.41 cm

Correct answer: B

Explanation: l² + b² = 41 and lb = 20. (l + b)² = l² + 2lb + b² = 41 + 40 = 81. So l + b = 9. Perimeter = 2 × 9 = 18 cm.

Question 32

Mathematics · 1 marks · −0.25

The mean of 5, 7, 9, x, and 11 is 8. The value of x is:

  1. A.6
  2. B.8
  3. C.10
  4. D.12

Correct answer: B

Explanation: Sum = 5 + 7 + 9 + x + 11 = 32 + x. Mean = (32 + x)/5 = 8. So 32 + x = 40, x = 8.

Question 33

Mathematics · 1 marks · −0.25

The median of the data 3, 7, 9, 11, 13, 17 is:

  1. A.9
  2. B.10
  3. C.11
  4. D.13

Correct answer: B

Explanation: Even number of observations (6). Median = average of 3rd and 4th values = (9 + 11)/2 = 10.

Question 34

Mathematics · 1 marks · −0.25

The mode of the data set 2, 3, 4, 4, 5, 5, 5, 6, 7 is:

  1. A.4
  2. B.5
  3. C.6
  4. D.3

Correct answer: B

Explanation: Mode is the value with the highest frequency. 5 appears 3 times (most frequent). Mode = 5.

Question 35

Mathematics · 1 marks · −0.25

If the mean of the data 6, 7, x, 8, y, 14 is 9, then the value of (x + y) is:

  1. A.19
  2. B.21
  3. C.23
  4. D.25

Correct answer: A

Explanation: Mean = (6 + 7 + x + 8 + y + 14)/6 = 9. So 35 + x + y = 54. x + y = 19.

Question 36

Mathematics · 1 marks · −0.25

The empirical relationship between mean, median, and mode is:

  1. A.Mode = 3 × Median − 2 × Mean
  2. B.Mode = 2 × Median − 3 × Mean
  3. C.Mean = 3 × Median − 2 × Mode
  4. D.Median = 3 × Mean − 2 × Mode

Correct answer: A

Explanation: The empirical formula is Mode = 3 × Median − 2 × Mean. This is used when the data is moderately asymmetrical.

Question 37

Mathematics · 1 marks · −0.25

The mean of the first 10 natural numbers is:

  1. A.5
  2. B.5.5
  3. C.6
  4. D.6.5

Correct answer: B

Explanation: Sum of first 10 natural numbers = 10 × 11/2 = 55. Mean = 55/10 = 5.5.

View all papers — UPSSSC PET (Preliminary Eligibility Test)

Practice this paper with a timer

Attempt it online, get scored instantly, and see which subjects are costing you marks.

Start practising free