TNPSC Maths Questions with Answers: 25 Solved Aptitude and Reasoning Problems for Group 4

Our Group 4 study plan gives Part C about 35 minutes, with 65 minutes each for Parts A and B and 15 minutes to check the answer sheet. That works out to about 84 seconds a question, but not every question needs the same time.

1. First pass: the quick ones. Series, coding, dice and one-step percentage questions often take under 30 seconds once you see the pattern. Do them first.

2. Second pass: the ones with working. Interest, area and time and work need a line or two on paper. Write each step; the step you do in your head is where slips creep in.

3. Last two minutes: no blanks. Any question still open gets a guess. A wrong guess costs nothing, the same as shading E, and a right one earns 1.5 marks.

Now the problems. Cover the answer under each one, give yourself about a minute, and write your choice down before you look.

1. Simplify: 48 ÷ 6 × 2 + 15 − 3 × 4

(A) 7 · (B) 19 · (C) 112 · (D) 31

Answer: (B) 19. Division and multiplication come first, left to right: 48 ÷ 6 = 8, 8 × 2 = 16 and 3 × 4 = 12. Then 16 + 15 − 12 = 19. Option (A) comes from doing 6 × 2 before the division.

2. Simplify: 0.6 × 0.6 + 0.4 × 0.4 + 2 × 0.6 × 0.4

(A) 0.52 · (B) 1 · (C) 0.1 · (D) 0.48

Answer: (B) 1. This is a² + b² + 2ab with a = 0.6 and b = 0.4, which equals (a + b)² = 1² = 1. Spot the identity and there is nothing to multiply. Option (A) forgets the 2ab term.

3. What per cent of 2.5 kg is 750 g?

(A) 0.3% · (B) 3% · (C) 30% · (D) 300%

Answer: (C) 30%. Put both in grams first: 750 ÷ 2,500 × 100 = 30%. Option (D) comes from taking 2.5 kg as 250 g.

4. A village has 8,000 people, and 55% of them are men. If 40% of the men and 30% of the women can read and write, how many people in the village are literate?

(A) 2,800 · (B) 2,840 · (C) 2,760 · (D) 1,760

Answer: (B) 2,840. Men: 4,400, and 40% of them is 1,760. Women: 3,600, and 30% of them is 1,080. Total 2,840. Option (A) averages the two percentages, which works only when there are as many men as women.

More methods: percentage shortcuts with 15 solved questions.

5. The HCF of two numbers is 12 and their LCM is 360. If one number is 72, what is the other?

(A) 30 · (B) 48 · (C) 60 · (D) 90

Answer: (C) 60. For two numbers, HCF × LCM = the product of the numbers, so the other is 12 × 360 ÷ 72 = 60. Check: the HCF of 72 and 60 is 12.

6. Three bells ring at intervals of 12, 18 and 24 minutes. They ring together at 8:00 AM. When will they next ring together?

(A) 8:06 AM · (B) 8:48 AM · (C) 9:12 AM · (D) 9:00 AM

Answer: (C) 9:12 AM. They meet again after the LCM of 12, 18 and 24, which is 72 minutes, so 1 hour 12 minutes after 8:00. Option (A) uses the HCF, 6. "Together again" questions always need the LCM.

7. ₹5,400 is divided among A, B and C in the ratio 2 : 3 : 4. What is C's share?

(A) ₹1,200 · (B) ₹1,800 · (C) ₹2,400 · (D) ₹2,700

Answer: (C) ₹2,400. The ratio has 2 + 3 + 4 = 9 parts, so one part is ₹600 and C gets 4 × 600. Options (A) and (B) are the shares of A and B.

8. The ages of a father and his son are in the ratio 7 : 2. After 10 years, the ratio will be 9 : 4. What is the son's present age?

(A) 10 years · (B) 15 years · (C) 20 years · (D) 35 years

Answer: (A) 10 years. Let the ages be 7x and 2x. Then (7x + 10) ÷ (2x + 10) = 9 ÷ 4, so 28x + 40 = 18x + 90 and x = 5: son 10, father 35. Testing the options is faster: a son of 10 means a father of 35, and in 10 years 45 : 20 is 9 : 4. Option (C) is the son's age after 10 years.

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

(A) 16 years · (B) 24 years · (C) 32 years · (D) 12 years

Answer: (B) 24 years. Doubling means the interest equals the principal in 8 years. Four times needs interest of three times the principal, so 3 × 8 = 24 years. Option (A) treats simple interest as if it compounds. It is also the time from doubling to four times, not from the start.

10. Find the compound interest on ₹10,000 at 10% per annum for 3 years, compounded annually.

(A) ₹3,000 · (B) ₹3,310 · (C) ₹2,100 · (D) ₹13,310

Answer: (B) ₹3,310. The amount is 10,000 × 1.1 × 1.1 × 1.1 = ₹13,310, so the interest is ₹3,310. Option (A) is the simple interest, (C) the compound interest for 2 years and (D) the amount, not the interest.

11. The difference between the compound interest and the simple interest on a sum for 2 years at 5% per annum is ₹15. What is the sum?

(A) ₹3,000 · (B) ₹6,000 · (C) ₹12,000 · (D) ₹1,500

Answer: (B) ₹6,000. For 2 years, CI − SI = P × (R/100)², so 15 = P × 1/400 and P = ₹6,000. Check: the simple interest is ₹600 and the compound interest ₹615.

12. The circumference of a circular park is 88 m. What is its area? (Take π = 22/7.)

(A) 154 m² · (B) 616 m² · (C) 2,464 m² · (D) 308 m²

Answer: (B) 616 m². From 2πr = 88, r = 88 × 7 ÷ 44 = 14 m, and the area is 22/7 × 14 × 14 = 616 m². Option (C) uses the diameter, 28 m, as the radius.

13. A path 2 m wide runs around the outside of a rectangular garden 20 m long and 15 m wide. What is the area of the path?

(A) 140 m² · (B) 156 m² · (C) 124 m² · (D) 74 m²

Answer: (B) 156 m². With the path, the outer rectangle is 24 m × 19 m = 456 m²; take away the garden's 300 m². Quick method for a path of width w outside: 2w(l + b) + 4w² = 140 + 16. Option (A) forgets the four corner squares, and (C) is the answer for a path inside the garden.

14. A cylindrical water tank has a radius of 7 m and a height of 10 m. How many litres of water can it hold? (Take π = 22/7.)

(A) 1,540 litres · (B) 15,400 litres · (C) 1,54,000 litres · (D) 15,40,000 litres

Answer: (D) 15,40,000 litres. The volume is πr²h = 22/7 × 7 × 7 × 10 = 1,540 m³, and 1 m³ holds 1,000 litres. Option (A) stops at cubic metres; capacity questions often hide a change of unit.

15. A can finish a job in 12 days and B in 24 days. Working together, in how many days will they finish it?

(A) 6 days · (B) 8 days · (C) 18 days · (D) 36 days

Answer: (B) 8 days. Together they take ab ÷ (a + b) = 12 × 24 ÷ 36 = 8 days. Check: A does 2/24 of the job a day and B 1/24, so together 3/24 = 1/8. Option (C) is the average, which can't be right: two people together must be faster than the faster one alone.

16. 12 workers can build a wall in 15 days. How many days will 18 workers take to build the same wall?

(A) 10 days · (B) 12 days · (C) 22½ days · (D) 9 days

Answer: (A) 10 days. The job is 12 × 15 = 180 worker-days, and 180 ÷ 18 = 10. More workers means fewer days; option (C) treats it as direct proportion.

The 10 reasoning questions need no formulas, only the habit of checking differences and ratios first.

17. Find the next number: 3, 7, 15, 31, 63, ?

(A) 95 · (B) 126 · (C) 127 · (D) 125

Answer: (C) 127. Each term is twice the previous one plus 1: 63 × 2 + 1 = 127. The differences, 4, 8, 16, 32, also double, so the next difference is 64.

18. Find the wrong number in the series: 1, 4, 9, 16, 23, 36

(A) 16 · (B) 23 · (C) 36 · (D) 9

Answer: (B) 23. These are the squares of 1 to 6, so the fifth term should be 25.

19. Find the next term: A1, C3, F6, J10, ?

(A) N14 · (B) O14 · (C) O15 · (D) P16

Answer: (C) O15. The numbers rise by 2, 3, 4 and then 5, giving 15, and each letter stands at that position in the alphabet: A is 1st, C 3rd, F 6th, J 10th and O 15th. Learn E = 5, J = 10, O = 15, T = 20 and Y = 25; they make these questions quick.

20. In a code, MADRAS is written as NBESBT. How is CHENNAI written in that code?

(A) DIFOOBK · (B) BGDMMZH · (C) DIFOOBJ · (D) DIFNOBJ

Answer: (C) DIFOOBJ. Each letter moves one place forward: M to N, A to B, and so on. So C becomes D, H becomes I, E becomes F, each N becomes O, A becomes B and I becomes J. Option (B) shifts backwards.

21. Three views of the same die show these faces meeting at a corner: 1, 2 and 3; then 3, 4 and 5; then 1, 3 and 5. Which number is opposite 1?

(A) 4 · (B) 5 · (C) 6 · (D) 2

Answer: (A) 4. Faces seen together can't be opposite each other. 3 is seen next to 1, 2, 4 and 5, so 6 is opposite 3. 1 is seen next to 2, 3 and 5, and 6 is taken, so 4 is opposite 1 (which leaves 2 opposite 5). Option (C) uses the 'opposite faces add up to 7' rule, which holds only for a standard die; this one isn't.

22. On a standard die, opposite faces add up to 7. The die rests on a table with 4 on top. What is the total of the four side faces?

(A) 10 · (B) 14 · (C) 17 · (D) 21

Answer: (B) 14. All six faces add up to 1 + 2 + 3 + 4 + 5 + 6 = 21. The top and bottom are opposite faces and make 7, so the sides make 21 − 7 = 14, whichever number is on top. Option (C) subtracts only the top face.

23. Pointing to a man, Priya said, "His mother is the only daughter of my mother." How is the man related to Priya?

(A) Brother · (B) Son · (C) Nephew · (D) Cousin

Answer: (B) Son. The only daughter of Priya's mother is Priya herself, so Priya is the man's mother. Work relation questions from the end of the sentence back to the speaker.

24. Five friends, Arun, Bala, Chitra, Divya and Ezhil, sit in a row facing north. Chitra is in the middle. Arun is immediately to Chitra's left. Bala is at the right end. Divya is not next to Bala. Who sits between Chitra and Bala?

(A) Arun · (B) Divya · (C) Ezhil · (D) Nobody

Answer: (C) Ezhil. Number the seats 1 to 5 from the left: Chitra is in 3, Arun in 2 and Bala in 5. Divya can't take seat 4, next to Bala, so she is in seat 1 and Ezhil in seat 4. Draw the five seats before you place anyone.

25. In a mirror, a wall clock appears to show 3:40. What is the actual time?

(A) 9:20 · (B) 8:20 · (C) 8:40 · (D) 3:20

Answer: (B) 8:20. For a mirror image, subtract the time you see from 11:60 (that is, 12:00): 11:60 − 3:40 = 8:20. Check: the mirror image of 8:20 is 3:40.

Count a guessed answer as wrong when you score yourself. A lucky guess is still a gap.

• Start with the textbooks. The Samacheer Kalvi maths books for Classes 6 to 10 teach every Part C aptitude topic at TNPSC's level; our Group 4 books guide says which to open.

• Keep a one-page formula sheet: HCF × LCM, simple and compound interest, the area and volume formulas, ab ÷ (a + b). Six of the most used are in our TNPSC shortcuts in Tamil post.

• Do 15 TNPSC aptitude questions a day, timed, and keep a list of the mistakes you repeat. The usual entries: units, the base of a percentage, LCM versus HCF.

• Put them back into full tests. In the exam, Part C shares three hours with 175 other questions. Once a week, sit a full-length timed paper and hold yourself to 35 minutes for Part C.

Thervu's Group 4 mock tests are timed, come in Tamil and English, and are marked the moment you submit, with the correct answer shown for each question. An explanation for every answer comes with Pro.