Q1. The price of an item rises from ₹400 to ₹500. What is the percentage increase?
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Answer: C. 25%
Increase = 500 − 400 = 100. % increase = 100/400 × 100 = 25%.
SSC CGL Quantitative Aptitude Intermediate Practice Set 3
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Percentage, Profit and Loss, Discount, Simple Interest, Compound Interest, Average, Ratio and Proportion, Time and Work, Speed, Time and Distance, LCM and HCF, Number System, Algebra, Problems on Ages, Mensuration, Geometry, Mixture and Alligation, Partnership, Simplification
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Q2. A shopkeeper buys a watch for ₹1500 and sells it for ₹1125. Find the profit or loss percentage.
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Answer: B. 25% loss
Loss = |1125 − 1500| = ₹375. Loss% = 375/1500 × 100 = 25%.
Q3. The marked price of a shirt is ₹8500. A discount of 25% is given. What is the selling price (in ₹)?
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Answer: A. 6375
SP = 8500 × 75/100 = ₹6375.
Q4. A sum of ₹2500 amounts to ₹3625 in 3 years at simple interest. What is the rate of interest per annum?
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Answer: C. 15%
SI = 3625 − 2500 = ₹1125. R = 1125 × 100 / (2500 × 3) = 15%.
Q5. Find the compound interest on ₹5000 for 2 years at 10% per annum, compounded annually (in ₹).
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Answer: D. 1050
Amount = 5000 × (110/100)² = ₹6050. CI = 6050 − 5000 = ₹1050.
Q6. The average age of 30 students in a class is 39 years. When the teacher's age is included, the average increases by 1 year. What is the teacher's age?
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Answer: C. 70 years
Teacher's age = (30 + 1) × 40 − 30 × 39 = 1240 − 1170 = 70 years.
Q7. If A:B = 2:5 and B:C = 5:6, find A:B:C.
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Answer: D. 2:5:6
Multiply the first ratio by 5 and the second by 5: A:B:C = 10:25:30 = 2:5:6.
Q8. A and B together can finish a job in 8 days. A alone can finish it in 12 days. How many days will B alone take?
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Answer: C. 24 days
B's work per day = 1/8 − 1/12 = 1/24. So B alone takes 24 days.
Q9. A train 200 m long runs at 45 km/h. How long will it take to cross a platform 125 m long?
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Answer: C. 26 seconds
Speed = 45 × 5/18 = 12.5 m/s. Distance = 200 + 125 = 325 m. Time = 325/12.5 = 26 s.
Q10. What is the least number which, when divided by 30, 8 and 25, leaves a remainder of 6 in each case?
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Answer: A. 606
LCM(30, 8, 25) = 600. Required number = 600 + 6 = 606.
Q11. What is the unit digit of 3^97?
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Answer: B. 3
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 97 leaves remainder 1 on division by 4, so take the 1st value in the cycle: 3.
Q12. If a + b = 6 and ab = 7, find a² + b².
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Answer: B. 22
a² + b² = (a + b)² − 2ab = 36 − 14 = 22.
Q13. A father's age is 3 times his son's age. After 14 years, the father will be 2 times as old as his son. What is the son's present age?
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Answer: D. 14 years
3x + 14 = 2x + 28 ⇒ x = 14 ⇒ x = 14 years.
Q14. Find the area of a circle of radius 28 cm. (Take π = 22/7)
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Answer: D. 2464 cm²
Area = 22/7 × 28 × 28 = 2464 cm².
Q15. What is the measure of each interior angle of a regular polygon with 10 sides?
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Answer: C. 144°
(10 − 2) × 180/10 = 144°.
Q16. In what ratio must rice at ₹15/kg be mixed with rice at ₹25/kg so that the mixture costs ₹24/kg?
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Answer: C. 1:9
Ratio = (25 − 24) : (24 − 15) = 1:9.
Q17. A invests ₹60000 for 8 months and B invests ₹55000 for 6 months. Out of a total profit of ₹30240, what is A's share (in ₹)?
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Answer: A. 17920
Ratio = 60000×8 : 55000×6 = 16:11. A's share = 30240 × 16/27 = ₹17920.
Q18. Find the value of √961 + 6².
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Answer: C. 67
√961 = 31; 6² = 36; total = 67.
Q19. The price of an item rises from ₹950 to ₹1045. What is the percentage increase?
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Answer: A. 10%
Increase = 1045 − 950 = 95. % increase = 95/950 × 100 = 10%.
Q20. A shopkeeper buys a watch for ₹1350 and sells it for ₹1215. Find the profit or loss percentage.
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Answer: C. 10% loss
Loss = |1215 − 1350| = ₹135. Loss% = 135/1350 × 100 = 10%.
Q21. The marked price of a shirt is ₹3000. A discount of 20% is given. What is the selling price (in ₹)?
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Answer: A. 2400
SP = 3000 × 80/100 = ₹2400.
Q22. A sum of ₹17000 amounts to ₹29750 in 5 years at simple interest. What is the rate of interest per annum?
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Answer: B. 15%
SI = 29750 − 17000 = ₹12750. R = 12750 × 100 / (17000 × 5) = 15%.
Q23. Find the compound interest on ₹3000 for 2 years at 20% per annum, compounded annually (in ₹).
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Answer: A. 1320
Amount = 3000 × (120/100)² = ₹4320. CI = 4320 − 3000 = ₹1320.
Q24. The average age of 40 students in a class is 51 years. When the teacher's age is included, the average increases by 1 year. What is the teacher's age?
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Answer: A. 92 years
Teacher's age = (40 + 1) × 52 − 40 × 51 = 2132 − 2040 = 92 years.
Q25. If A:B = 4:5 and B:C = 7:6, find A:B:C.
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Answer: A. 28:35:30
Multiply the first ratio by 7 and the second by 5: A:B:C = 28:35:30 = 28:35:30.