Q1. Find the value of √625 + 3².
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Answer: C. 34
√625 = 25; 3² = 9; total = 34.
SSC CGL Quantitative Aptitude Intermediate Practice Set 5
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Simplification, 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
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Q2. The price of an item rises from ₹1000 to ₹1250. What is the percentage increase?
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Answer: D. 25%
Increase = 1250 − 1000 = 250. % increase = 250/1000 × 100 = 25%.
Q3. A shopkeeper buys a watch for ₹900 and sells it for ₹810. Find the profit or loss percentage.
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Answer: A. 10% loss
Loss = |810 − 900| = ₹90. Loss% = 90/900 × 100 = 10%.
Q4. The marked price of a shirt is ₹9500. A discount of 15% is given. What is the selling price (in ₹)?
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Answer: B. 8075
SP = 9500 × 85/100 = ₹8075.
Q5. A sum of ₹4500 amounts to ₹5400 in 4 years at simple interest. What is the rate of interest per annum?
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Answer: A. 5%
SI = 5400 − 4500 = ₹900. R = 900 × 100 / (4500 × 4) = 5%.
Q6. Find the compound interest on ₹4000 for 2 years at 5% per annum, compounded annually (in ₹).
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Answer: A. 410
Amount = 4000 × (105/100)² = ₹4410. CI = 4410 − 4000 = ₹410.
Q7. The average age of 30 students in a class is 27 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. 58 years
Teacher's age = (30 + 1) × 28 − 30 × 27 = 868 − 810 = 58 years.
Q8. If A:B = 6:7 and B:C = 5:6, find A:B:C.
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Answer: A. 30:35:42
Multiply the first ratio by 5 and the second by 7: A:B:C = 30:35:42 = 30:35:42.
Q9. A and B together can finish a job in 9 days. A alone can finish it in 12 days. How many days will B alone take?
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Answer: C. 36 days
B's work per day = 1/9 − 1/12 = 1/36. So B alone takes 36 days.
Q10. A train 200 m long runs at 36 km/h. How long will it take to cross a platform 350 m long?
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Answer: A. 55 seconds
Speed = 36 × 5/18 = 10 m/s. Distance = 200 + 350 = 550 m. Time = 550/10 = 55 s.
Q11. What is the least number which, when divided by 8, 12 and 15, leaves a remainder of 6 in each case?
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Answer: A. 126
LCM(8, 12, 15) = 120. Required number = 120 + 6 = 126.
Q12. What is the unit digit of 17^114?
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Answer: A. 9
Unit digits of 7^1, ^2, ^3, ^4 are 7, 9, 3, 1. 114 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q13. If a + b = 12 and ab = 10, find a² + b².
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Answer: C. 124
a² + b² = (a + b)² − 2ab = 144 − 20 = 124.
Q14. A father's age is 4 times his son's age. After 4 years, the father will be 3 times as old as his son. What is the son's present age?
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Answer: B. 8 years
4x + 4 = 3x + 12 ⇒ x = 8 ⇒ x = 8 years.
Q15. Find the circumference of a circle of radius 35 cm. (Take π = 22/7)
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Answer: D. 220 cm
C = 2 × 22/7 × 35 = 220 cm.
Q16. What is the measure of each interior angle of a regular polygon with 12 sides?
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Answer: C. 150°
(12 − 2) × 180/12 = 150°.
Q17. In what ratio must rice at ₹10/kg be mixed with rice at ₹20/kg so that the mixture costs ₹11/kg?
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Answer: B. 9:1
Ratio = (20 − 11) : (11 − 10) = 9:1.
Q18. A invests ₹10000 for 9 months and B invests ₹25000 for 6 months. Out of a total profit of ₹9624, what is A's share (in ₹)?
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Answer: A. 3609
Ratio = 10000×9 : 25000×6 = 3:5. A's share = 9624 × 3/8 = ₹3609.
Q19. Find the value of √529 + 2².
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Answer: B. 27
√529 = 23; 2² = 4; total = 27.
Q20. A shopkeeper buys a watch for ₹1900 and sells it for ₹1710. Find the profit or loss percentage.
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Answer: D. 10% loss
Loss = |1710 − 1900| = ₹190. Loss% = 190/1900 × 100 = 10%.
Q21. The marked price of a shirt is ₹9500. A discount of 25% is given. What is the selling price (in ₹)?
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Answer: A. 7125
SP = 9500 × 75/100 = ₹7125.
Q22. A sum of ₹9500 amounts to ₹12540 in 4 years at simple interest. What is the rate of interest per annum?
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Answer: B. 8%
SI = 12540 − 9500 = ₹3040. R = 3040 × 100 / (9500 × 4) = 8%.
Q23. Find the compound interest on ₹18000 for 2 years at 20% per annum, compounded annually (in ₹).
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Answer: A. 7920
Amount = 18000 × (120/100)² = ₹25920. CI = 25920 − 18000 = ₹7920.
Q24. The average age of 25 students in a class is 45 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: B. 71 years
Teacher's age = (25 + 1) × 46 − 25 × 45 = 1196 − 1125 = 71 years.
Q25. If A:B = 4:5 and B:C = 2:3, find A:B:C.
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Answer: A. 8:10:15
Multiply the first ratio by 2 and the second by 5: A:B:C = 8:10:15 = 8:10:15.