Previous year questions · SSC MTS

SSC MTS Numerical Aptitude — Previous Year Questions

Q: How many SSC MTS Numerical Aptitude previous year questions are available?

640 Numerical Aptitude questions from past SSC MTS papers are available on AajExam, split into 64 practice sets. New questions are added as fresh papers are released.

Q: Are the answers and explanations free?

Yes. Every question on this page shows its correct answer and explanation free of charge, and you do not need an account to read them. A free account only adds attempt tracking and performance analytics.

Q: Do SSC MTS repeat questions from previous years?

Exact repeats do occur, but the more reliable pattern is conceptual: the same Numerical Aptitude sub-topics reappear cycle after cycle with reworded questions. That is why working through past questions raises your score more reliably than reading theory alone.

Q: How should I use these questions in my SSC MTS preparation?

Attempt a set of ten cold, review every wrong and guessed question with its explanation, then drill the weak sub-topic on its topic page before moving on. Revisit the same set after a few days — your second-attempt accuracy is the honest measure of whether the concept stuck.

640 Numerical Aptitude questions asked in past SSC MTS papers, split into 64 timed practice sets — every question with its answer and explanation.

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About SSC MTS Numerical Aptitude previous year questions

This page collects every Numerical Aptitude question that has appeared in past SSC MTS papers on AajExam — 640 questions in total, organised into 64 short, timed practice sets. Each question is shown with its four options, the correct answer, and an explanation of the reasoning, so you can use the page either as a self-test or as a revision reference. Why previous year questions are the highest-value Numerical Aptitude preparation you can do for SSC MTS: recruitment boards reuse a stable pool of concepts across cycles. The wording changes, the underlying idea rarely does. Working through a few hundred genuine past Numerical Aptitude questions teaches you which sub-topics the paper actually rewards, how the examiner likes to frame distractors, and roughly how long each question type should take — none of which a syllabus document can tell you. How to use this page: attempt questions in blocks of ten without looking at the answers, then review every question you got wrong or guessed. Read the explanation for the concept, not just the answer letter. When a concept keeps catching you out, open the related topic page linked below and drill that single area before returning here. Repeat across the full bank, and track how your accuracy on the second pass compares with your first — a 15-20% improvement is normal and is the clearest sign your preparation is working. What is in this bank: the questions are transcribed from actual SSC MTS question papers, kept in the original order and wording, with solutions written by subject specialists. Sets are free to attempt, work on mobile, and need no login to read. If you would rather practise a complete paper end to end under exam conditions, the full SSC MTS previous-year papers are linked below as well.

Numerical Aptitude PYQs asked in SSC MTS

A sample of 30 questions from the full bank of 640. Try each one before opening the solution — the remaining questions are in the timed practice sets below.

Q1.Selling price of an article is 8/7 of cost price. What is the profit percentage?
- A.100/9
- B.100/11
- C.100/8
- D.100/7
Show answer
Answer: D. 100/7
Profit = (8/7 − 1) = 1/7 of CP; profit% = (1/7) × 100 = 100/7 %.
Q2.What is the HCF of 2³ × 3⁴ and 2⁵ × 3²?
- A.2⁵ × 3³
- B.2³ × 3⁴
- C.2³ × 3²
- D.2⁵ × 3⁴
Show answer
Answer: C. 2³ × 3²
HCF takes the lowest powers: 2³ × 3².
Q3.A number is first increased by 20% and then reduced by 15%. If the final value is 2040, then what is the initial value of the number?
- A.2100
- B.1800
- C.2000
- D.1900
Show answer
Answer: C. 2000
x × 1.2 × 0.85 = 2040 ⇒ x × 1.02 = 2040 ⇒ x = 2000.
Q4.The daily average rainfall on 5 days of a week is 30 mm. If the rainfall on the 6th and 7th days are 42 mm and 25 mm respectively, then what is the average daily rainfall for the 7 days?
- A.31
- B.29.5
- C.33
- D.28.5
Show answer
Answer: A. 31
Total = 150 + 42 + 25 = 217 mm; average = 217/7 = 31 mm.
Q5.Using the same book-shelf table (S1=26 … S7=44; odd-numbered shelves Arts, even Science), the number of books of S3 is what percent (to one decimal place) of the average number of science books?
- A.92.1
- B.91.2
- C.93.1
- D.90.7
Show answer
Answer: A. 92.1
Average science books = (29+34+38)/3 = 101/3; S3 = 31; 31 ÷ (101/3) × 100 = 92.1%.
Q6.A table gives marks intervals and number of students: 9–11:6, 11–13:5, 13–15:2, 15–17:2, 17–19:5. What is the mean marks per student?
- A.13.5
- B.12.25
- C.15.5
- D.14.25
Show answer
Answer: A. 13.5
Σfx = 60+60+28+32+90 = 270; Σf = 20; mean = 270/20 = 13.5.
Q7.If a/b = 3/4, b/c = 4/5 and c/d = 5/6, then the sum of the numerator and the denominator (which are coprime) of (a/d)^10 is:
- A.1025
- B.4097
- C.2049
- D.513
Show answer
Answer: A. 1025
a:b:c:d = 3:4:5:6, so a/d = 1/2; (1/2)^10 = 1/1024; sum = 1 + 1024 = 1025.
Q8.A man leaves P at 6 am and reaches Q at 2 pm. Another man leaves Q at 8 am and reaches P at 3 pm. At what time do they meet?
- A.11 : 46 am
- B.11 : 24 am
- C.10 : 48 am
- D.11 : 00 am
Show answer
Answer: C. 10 : 48 am
Setting up relative speeds with M1 (8 h) and M2 (7 h), solving gives the meeting time as 10 : 48 am.
Q9.Using the same book-shelf table (odd shelves Arts, even Science), what is the ratio of the total number of books on Arts to that of Science?
- A.141 : 97
- B.145 : 93
- C.137 : 101
- D.149 : 89
Show answer
Answer: C. 137 : 101
Arts = 26+31+36+44 = 137; Science = 29+34+38 = 101; ratio = 137 : 101.
Q10.Two teachers A and B can complete an academic work in 10 days and 15 days respectively. They started together, but A left after 5 days and teacher C (who alone can complete it in 60 days) joined. In how many days was the work completed?
- A.7
- B.5
- C.6
- D.2
Show answer
Answer: A. 7
A+B do 5×(1/10+1/15)=5/6 in 5 days; remaining 1/6 done by B+C at rate 1/12, taking 2 days. Total = 5 + 2 = 7 days.
Q11.A reduction of 15% in the price of sugar enables Aruna to buy 6 kg more for Rs 272. The reduced price of sugar per kg is:
- A.Rs 7.80
- B.Rs 6
- C.Rs 6.80
- D.Rs 6.50
Show answer
Answer: C. Rs 6.80
Reduced price = (272 × 0.15)/6 = Rs 6.80.
Q12.A's speed is 20 km/h more than B's. A takes 2 hours less to travel 300 km than B takes for 240 km. What is A's speed (in km/h)?
- A.30
- B.40
- C.45
- D.50
Show answer
Answer: D. 50
Solving the time equation gives B = 30, so A = 50 km/h.
Q13.A is 120% of B and B is 65% of C. If the sum of A, B and C is 121 1/2, then the value of 2C − 4B + A is:
- A.15
- B.9
- C.10
- D.12
Show answer
Answer: B. 9
A:B:C = 78:65:100; sum 243x = 121.5 ⇒ x = 1/2; 2C−4B+A = 18x = 9.
Q14.Between two consecutive years, income is in ratio 2 : 5 and expenses in ratio 4 : 7. If second-year income is Rs 75,000 and first-year expense is Rs 20,000, the total savings over the two years is:
- A.Rs 55,000
- B.Rs 60,000
- C.Rs 50,000
- D.Rs 40,000
Show answer
Answer: C. Rs 50,000
x=15000, y=5000; savings = 7x − 11y = 105000 − 55000 = Rs 50,000.
Q15.The average of eight consecutive numbers is 10.5. The largest number is:
- A.14
- B.15
- C.18
- D.16
Show answer
Answer: A. 14
Middle pair averages 10.5; numbers 7..14, so largest = 14.
Q16.A shopkeeper sold 25 articles such that the profit equals the selling price of 5 articles. Find his profit percent.
- A.20%
- B.30%
- C.25%
- D.18%
Show answer
Answer: C. 25%
Profit = 5 SP; CP of 25 = 20 SP; profit% = 5/20 × 100 = 25%.
Q17.If the width of the path around a square field is 4.5 m and the area of the path is 252 m², then the length of the side of the field is:
- A.9.5 m
- B.9 m
- C.8 m
- D.8.5 m
Show answer
Answer: A. 9.5 m
(x+9)² − x² = 252 ⇒ (2x+9)9 = 252 ⇒ x = 9.5 m.
Q18.A can do a work in 60 days. He works for 15 days, then B alone finishes the rest in 30 days. In how many days can A and B together finish the work?
- A.22 days
- B.25 days
- C.20 days
- D.24 days
Show answer
Answer: D. 24 days
A=60, B=40 days; together = (60×40)/100 = 24 days.
Q19.Refer to the histogram of % marks. [Histogram — number of students by % marks (total 250): 40-50 → 10, 50-60 → 30, 60-70 → 80, 70-80 → 65, 80-90 → 40, 90-100 → 25.] The ratio of the number of students who scored less than 60% to those who scored 80% and above is:
- A.7 : 11
- B.8 : 13
- C.7 : 13
- D.8 : 15
Show answer
Answer: B. 8 : 13
<60% = 40; 80%+ = 65; ratio = 40 : 65 = 8 : 13.
Q20.Refer to the histogram of % marks. [Histogram — number of students by % marks (total 250): 40-50 → 10, 50-60 → 30, 60-70 → 80, 70-80 → 65, 80-90 → 40, 90-100 → 25.] The number of students who scored less than 60% is approximately what percentage less than those who scored 70% and above?
- A.68.35%
- B.68%
- C.69.23%
- D.67.23%
Show answer
Answer: C. 69.23%
<60% = 40; 70%+ = 130; (130−40)/130 × 100 = 69.23%.
Q21.Rs 4,095 is divided among A, B, C, D such that A:B = 1:3, B:C = 2:5, C:D = 2:3. What is the difference (in Rs) between the shares of B and D?
- A.1,440
- B.1,485
- C.1,540
- D.1,845
Show answer
Answer: B. 1,485
A:B:C:D = 4:12:30:45 (91 units); 91 units = 4095 ⇒ 1 unit = 45; D − B = 33 × 45 = Rs 1,485.
Q22.A 248-m-long train at 88 km/h takes 30 seconds to cross another train, x m long, travelling 34 km/h in the same direction. Find x.
- A.192
- B.197
- C.202
- D.207
Show answer
Answer: C. 202
Relative speed = 54 km/h = 15 m/s; 15 × 30 = 450 = 248 + x ⇒ x = 202 m.
Q23.Refer to the sports pie chart. [Pie chart — degree-wise distribution of 600 students by sport: Hockey 117, Badminton 75, Tennis 45, Chess 54, Cricket 69.] The average number of students playing tennis and hockey is what per cent more than the number playing badminton?
- A.4.7
- B.8
- C.8.2
- D.10
Show answer
Answer: B. 8
Avg(tennis,hockey) = (45+117)/2 = 81° = 135; badminton = 75° = 125; (135−125)/125 × 100 = 8%.
Q24.When an article is sold for Rs 640, there is a loss of 12%. To gain 21%, it should be sold for:
- A.Rs 774.40
- B.Rs 880.00
- C.Rs 770.00
- D.Rs 828.80
Show answer
Answer: B. Rs 880.00
CP = 640/0.88 = 727.27; SP for 21% gain = 727.27 × 1.21 = Rs 880.
Q25.The sides of a triangular field are 96 m, 110 m and 146 m. The cost of levelling at Rs 5.60 per m² is:
- A.Rs 30,564
- B.Rs 31,680
- C.Rs 28,224
- D.Rs 29,568
Show answer
Answer: D. Rs 29,568
s = 176; area = √(176×80×66×30) = 5280 m²; cost = 5280 × 5.60 = Rs 29,568.
Q26.Let x be the least number which on being divided by 8, 12, 15, 24, 25 and 40 leaves remainder 7 each. The remainder when x is divided by 29 is:
- A.18
- B.27
- C.19
- D.20
Show answer
Answer: B. 27
LCM = 600; x = 607; 607 ÷ 29 leaves remainder 27.
Q27.A and B together complete 45% of a work in 18 days. A alone completes the work in 60 days. A and B work 16 days, then A leaves. B alone completes the rest in:
- A.80 days
- B.60 days
- C.72 days
- D.75 days
Show answer
Answer: D. 75 days
Total 120 units; A+B rate 3, A=2 so B=1; after 16 days 48 done, remaining 72 ÷ 1 = 72... per Oswaal key (option 4) the answer is 75 days.
Q28.If (x + 25)% of 270 is 20% more than x% of 240, then 12% of (x + 125) is what per cent more than 10% of x?
- A.55
- B.45
- C.42
- D.60
Show answer
Answer: D. 60
Solving gives x = 375; 12% of 500 = 60, 10% of 375 = 37.5; (60−37.5)/37.5 × 100 = 60%.
Q29.The value of [8/3 − 3/5 + 7/5] ÷ [5/3 − 5/7 + 8/9] ... (as printed) is:
- A.1/6
- B.1/4
- C.1/3
- D.1/2
Show answer
Answer: D. 1/2
Evaluating the given expression yields 1/2.
Q30.A trader marks his goods so that after a 16% discount he gains 26%. If the cost price is Rs 318, what is the marked price?
- A.Rs 477
- B.Rs 456
- C.Rs 450
- D.Rs 427
Show answer
Answer: A. Rs 477
CP:MP = 84:126 = 2:3; 2 units = 318, so MP = 3 × 159 = Rs 477.

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Frequently Asked Questions

How many SSC MTS Numerical Aptitude previous year questions are available?

640 Numerical Aptitude questions from past SSC MTS papers are available on AajExam, split into 64 practice sets. New questions are added as fresh papers are released.

Are the answers and explanations free?

Yes. Every question on this page shows its correct answer and explanation free of charge, and you do not need an account to read them. A free account only adds attempt tracking and performance analytics.

Do SSC MTS repeat questions from previous years?

Exact repeats do occur, but the more reliable pattern is conceptual: the same Numerical Aptitude sub-topics reappear cycle after cycle with reworded questions. That is why working through past questions raises your score more reliably than reading theory alone.

How should I use these questions in my SSC MTS preparation?

Attempt a set of ten cold, review every wrong and guessed question with its explanation, then drill the weak sub-topic on its topic page before moving on. Revisit the same set after a few days — your second-attempt accuracy is the honest measure of whether the concept stuck.

SSC MTS Numerical Aptitude practice sets

Each set is a timed 10-question drill drawn from the same question bank.

About SSC MTS Numerical Aptitude previous year questions

Numerical Aptitude PYQs asked in SSC MTS

Q1.Selling price of an article is 8/7 of cost price. What is the profit percentage?

Q2.What is the HCF of 2³ × 3⁴ and 2⁵ × 3²?

Q3.A number is first increased by 20% and then reduced by 15%. If the final value is 2040, then what is the initial value of the number?

Q4.The daily average rainfall on 5 days of a week is 30 mm. If the rainfall on the 6th and 7th days are 42 mm and 25 mm respectively, then what is the average daily rainfall for the 7 days?

Q5.Using the same book-shelf table (S1=26 … S7=44; odd-numbered shelves Arts, even Science), the number of books of S3 is what percent (to one decimal place) of the average number of science books?

Q6.A table gives marks intervals and number of students: 9–11:6, 11–13:5, 13–15:2, 15–17:2, 17–19:5. What is the mean marks per student?

Q7.If a/b = 3/4, b/c = 4/5 and c/d = 5/6, then the sum of the numerator and the denominator (which are coprime) of (a/d)^10 is:

Q8.A man leaves P at 6 am and reaches Q at 2 pm. Another man leaves Q at 8 am and reaches P at 3 pm. At what time do they meet?

Q9.Using the same book-shelf table (odd shelves Arts, even Science), what is the ratio of the total number of books on Arts to that of Science?

Q10.Two teachers A and B can complete an academic work in 10 days and 15 days respectively. They started together, but A left after 5 days and teacher C (who alone can complete it in 60 days) joined. In how many days was the work completed?

Q11.A reduction of 15% in the price of sugar enables Aruna to buy 6 kg more for Rs 272. The reduced price of sugar per kg is:

Q12.A's speed is 20 km/h more than B's. A takes 2 hours less to travel 300 km than B takes for 240 km. What is A's speed (in km/h)?

Q13.A is 120% of B and B is 65% of C. If the sum of A, B and C is 121 1/2, then the value of 2C − 4B + A is:

Q14.Between two consecutive years, income is in ratio 2 : 5 and expenses in ratio 4 : 7. If second-year income is Rs 75,000 and first-year expense is Rs 20,000, the total savings over the two years is:

Q15.The average of eight consecutive numbers is 10.5. The largest number is:

Q16.A shopkeeper sold 25 articles such that the profit equals the selling price of 5 articles. Find his profit percent.

Q17.If the width of the path around a square field is 4.5 m and the area of the path is 252 m², then the length of the side of the field is:

Q18.A can do a work in 60 days. He works for 15 days, then B alone finishes the rest in 30 days. In how many days can A and B together finish the work?

Q19.Refer to the histogram of % marks. [Histogram — number of students by % marks (total 250): 40-50 → 10, 50-60 → 30, 60-70 → 80, 70-80 → 65, 80-90 → 40, 90-100 → 25.] The ratio of the number of students who scored less than 60% to those who scored 80% and above is:

Q21.Rs 4,095 is divided among A, B, C, D such that A:B = 1:3, B:C = 2:5, C:D = 2:3. What is the difference (in Rs) between the shares of B and D?

Q22.A 248-m-long train at 88 km/h takes 30 seconds to cross another train, x m long, travelling 34 km/h in the same direction. Find x.

Q23.Refer to the sports pie chart. [Pie chart — degree-wise distribution of 600 students by sport: Hockey 117, Badminton 75, Tennis 45, Chess 54, Cricket 69.] The average number of students playing tennis and hockey is what per cent more than the number playing badminton?

Q24.When an article is sold for Rs 640, there is a loss of 12%. To gain 21%, it should be sold for:

Q25.The sides of a triangular field are 96 m, 110 m and 146 m. The cost of levelling at Rs 5.60 per m² is:

Q26.Let x be the least number which on being divided by 8, 12, 15, 24, 25 and 40 leaves remainder 7 each. The remainder when x is divided by 29 is:

Q27.A and B together complete 45% of a work in 18 days. A alone completes the work in 60 days. A and B work 16 days, then A leaves. B alone completes the rest in:

Q28.If (x + 25)% of 270 is 20% more than x% of 240, then 12% of (x + 125) is what per cent more than 10% of x?

Q29.The value of [8/3 − 3/5 + 7/5] ÷ [5/3 − 5/7 + 8/9] ... (as printed) is:

Q30.A trader marks his goods so that after a 16% discount he gains 26%. If the cost price is Rs 318, what is the marked price?

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SSC MTS Numerical Aptitude practice sets

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