## SSC SI (CAPF/Delhi Police) Quantitative Aptitude Solved Paper

1. A trader lists his article 20% above the cost price and allows a discount of 10% on cash payment. His gain per cent is–

(A) 6% (B) 5% (C) 8% (D) 10% (

2. A chord of length 24 cm is at a distance of 5 cm form the centre of a circle. The length of the chord of the same circle which is at a distance of 12 cm from the centre is–

(A) 12 cm (B) 11 cm (C) 17 cm (D) 10 cm (

3. A sum of Rs.

(A) Rs. 16,000 (B) Rs. 24,000 (C) Rs. 20,000 (D) Rs. 36,000 (

4. If 3

(A) 17/15 (B) 15/34 (C) 15/17 (D) 17/30 (

5. The average monthly income of A and B is Rs. 15,050, the average monthly income of B and C is Rs. 15,350 and the average income of A and C is Rs. 15,200. The monthly income of A is–

(A) Rs. 14,900 (B) Rs. 15,500 (C) Rs. 15,900 (D) Rs. 15,200 (

6. If p, q, r are all real numbers, then (

(A) (

7. A number is increased by 15% and then decreased by 25% and the number becomes 22 less than the original number. The original number is–

(A) 140 (B) 160 (C) 100 (D) 120 (

8. By selling an article at 3/4 of selling price, a trader incurred a loss of 10%. The profit/loss percentage, when it is sold at the original selling price, is–

(A) 20% profit (B) 120% profit (C) 20% loss (D) 32.5% loss (

9. The average age of a class is 15.8 years. The average age of the boys in the class in 16.4 year while that of the girls is 15.4 years. The ratio of boys to girls in the class is–

(A) 3 : 4 (B) 2 : 3 (C) 1 : 2 (D) 3 : 5 (

10. A man travelled a distance of 72 km in 12 hours. He travelled partly on foot at 5 km/hour and partly on bicycle at 10 km/hour. The distance travelled on foot is–

(A) 46 km (B) 50 km (C) 48 km (D) 52 km (

11. If 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days, then 10 women will complete it in–

(A) 40 days (B) 45 days (C) 50 days (D) 35 days (

12. A can is full of a mixture of two liquids A and B in the ratio of 7 : 5. When 9 litres of mixture are drawn off from the can and replaced by the same quantity of liquid B, the ratio of A and B in the can becomes 7 : 9. The capacity of the can is–

(A) 10 litres (B) 20 litres (C) 21 litres (D) 36 litres (

13. A sum of money placed at compound interest double itself at 2 years. The year it will take to amount 4 times itself is–

(A) 3 b) 4 (C) 6 (D) 8 (

14. From the top and bottom of a straight hill the angle of depression and elevation of the top of a pillar of 10 m. height are observed to be 60° and 30° respectively. The height (in metres) of the hill is–

(A) 30 (B) 60 (C) 40 (D) 80 (

(A) 6% (B) 5% (C) 8% (D) 10% (

**Ans :**C)2. A chord of length 24 cm is at a distance of 5 cm form the centre of a circle. The length of the chord of the same circle which is at a distance of 12 cm from the centre is–

(A) 12 cm (B) 11 cm (C) 17 cm (D) 10 cm (

**Ans :**D)3. A sum of Rs.

*x*was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs. 300 more. The value of 4*x*is–(A) Rs. 16,000 (B) Rs. 24,000 (C) Rs. 20,000 (D) Rs. 36,000 (

**Ans :**C)4. If 3

*= 81 and 81*^{x + y}*= 3, then the value of*^{x – y}*x/y*is–(A) 17/15 (B) 15/34 (C) 15/17 (D) 17/30 (

**Ans :**A)5. The average monthly income of A and B is Rs. 15,050, the average monthly income of B and C is Rs. 15,350 and the average income of A and C is Rs. 15,200. The monthly income of A is–

(A) Rs. 14,900 (B) Rs. 15,500 (C) Rs. 15,900 (D) Rs. 15,200 (

**Ans :**A)6. If p, q, r are all real numbers, then (

*p – q*)^{3}+ (*q – r*)^{3}+ (*r – p*)^{3}is equal to–(A) (

*p – q*) (*q – r*) (*r – p*) (B) 1 (C) 3(*p – q*) (*q – r*) (*r – p*) (D) 0 (**Ans :**C)7. A number is increased by 15% and then decreased by 25% and the number becomes 22 less than the original number. The original number is–

(A) 140 (B) 160 (C) 100 (D) 120 (

**Ans :**B)8. By selling an article at 3/4 of selling price, a trader incurred a loss of 10%. The profit/loss percentage, when it is sold at the original selling price, is–

(A) 20% profit (B) 120% profit (C) 20% loss (D) 32.5% loss (

**Ans :**A)9. The average age of a class is 15.8 years. The average age of the boys in the class in 16.4 year while that of the girls is 15.4 years. The ratio of boys to girls in the class is–

(A) 3 : 4 (B) 2 : 3 (C) 1 : 2 (D) 3 : 5 (

**Ans :**B)10. A man travelled a distance of 72 km in 12 hours. He travelled partly on foot at 5 km/hour and partly on bicycle at 10 km/hour. The distance travelled on foot is–

(A) 46 km (B) 50 km (C) 48 km (D) 52 km (

**Ans :**C)11. If 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days, then 10 women will complete it in–

(A) 40 days (B) 45 days (C) 50 days (D) 35 days (

**Ans :**A)12. A can is full of a mixture of two liquids A and B in the ratio of 7 : 5. When 9 litres of mixture are drawn off from the can and replaced by the same quantity of liquid B, the ratio of A and B in the can becomes 7 : 9. The capacity of the can is–

(A) 10 litres (B) 20 litres (C) 21 litres (D) 36 litres (

**Ans :**D)13. A sum of money placed at compound interest double itself at 2 years. The year it will take to amount 4 times itself is–

(A) 3 b) 4 (C) 6 (D) 8 (

**Ans :**B)14. From the top and bottom of a straight hill the angle of depression and elevation of the top of a pillar of 10 m. height are observed to be 60° and 30° respectively. The height (in metres) of the hill is–

(A) 30 (B) 60 (C) 40 (D) 80 (

**Ans :**C)**Direction (Q. 15-19) :**Study the following table which shows the amount of money invested (Rupees in crore) in the core infrastructure areas of two districts, A and B of a State, and answer the given Questions.Core Area | District A | District B | ||

1995 | 1996 | 1995 | 1996 | |

Electricity Chemical Thermal Solar Nuclear | 815.2 389.5 632.4 468.1 617.9 | 1051.2 476.7 565.9 589.6 803.1 | 2065.8 745.3 1232.7 1363.5 1674.3 | 2365.1 986.4 1026.3 1792.1 2182.1 |

Total | 2923.1 | 3489.5 | 7081.6 | 8352.0 |

15. By approximately what per cent was the total investment in the two districts A and B more in 1996 as compared to 1995?

(A) 14% (B) 21% (C) 24% (D) 18% (

16. The total investment in electricity and thermal energy in 1995, in these two districts A and B formed approximately what per cent of the total investment made in that year?

(A) 55% (B) 41% (C) 52% (D) 47% (

17. In district B, the investment in which area in 1996 did show the highest percentage increase over the investment in that area in 1995?

(A) Electricity (B) Solar (C) Nuclear (D) Chemical (

18. Approximately how many times was the total investment in 1995 and 1996 in district B was that of total investment of district A in the same years?

(A) 2.8 (B) 1.9 (C) 2.4 (D) 1.7 (

19. If the total investment in district B shows the same rate of increase in 1997, as it had shown from 1995 to 1996, what approximately would be the total investment in B in 1997?

(A) Rs. 9,170 crore (B) Rs. 8,540 crore (C) Rs. 9,850 crore (D) Rs. 10,020 crore (

20. A man sells an article t 5% above the cost price. If he had bought it at 5% less than what he paid for it and sold it for Rs. 2 less, he would have gained 10%. The cost price of the article is–

(A) Rs. 250 (B) Rs. 400 (C) Rs. 200 (D) Rs. 350 (

21. The radii of the base of a cylinder and a cone are equal and their volumes are also equal. Then the ratio of their heights is–

(A) 1 : 4 (B) 2 : 1 (C) 1 : 2 (D) 1 : 3 (

22. If a person spends 40% of his income on food, 20% on house rent and 70% of the remaining on children's education, then the percentage of his income left is–

(A) 8% (B) 10% (C) 12% (D) 6% (

23. If tan θ + sec θ = 2, then the value of tan θ is–

(A) 2/3 (B) 3/5 (C) 3/4 (D) 4/5 (

24. Let

(A) 15 (B) 17 (C) 9 (D) 7 (

25. Points A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction, They meet in 5 hours. If the cars travel towards each other, they meet in 1 hour. What is the speed of the faster car?

(A) 80 km/hour (B) 40 km/hour (C) 70 km/hour (D) 60 km/hour (

26. A cylindrical rod of radius 30 cm and length 40 cm is melted and made into spherical balls of radius 1 cm. The number of spherical balls is–

(A) 40000 (B) 27000 (C) 36000 (D) 90000 (

27. A merchant purchases a wrist watch for Rs. 1,200 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. The list price of the watch is–

(A) Rs. 1,400 (B) Rs. 1,600 (C) Rs. 1,800 (D) Rs. 1,200 (

28. The sum of two numbers is 15⅓ and their difference is 4⅔. The product of the numbers is–

(A) 53 ⅓ (B) 60 (C) 48⅔ (D) 50 (

29. A and B can separately finish a piece of work in 20 days and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work is–

(A) 40 days (B) 60 days (C) 30 days (D) 50 days (

30. The ratio of the radii of two cylinders is 2 : 1 and their heights are in the ratio 3 : 2. Then their volumes are in the ratio–

(A) 6 : 1 (B) 4 : 3 (C) 6 : 5 (D) 3 : 1 (

-(A) 14% (B) 21% (C) 24% (D) 18% (

**Ans :**D)16. The total investment in electricity and thermal energy in 1995, in these two districts A and B formed approximately what per cent of the total investment made in that year?

(A) 55% (B) 41% (C) 52% (D) 47% (

**Ans :**D)17. In district B, the investment in which area in 1996 did show the highest percentage increase over the investment in that area in 1995?

(A) Electricity (B) Solar (C) Nuclear (D) Chemical (

**Ans :**D)18. Approximately how many times was the total investment in 1995 and 1996 in district B was that of total investment of district A in the same years?

(A) 2.8 (B) 1.9 (C) 2.4 (D) 1.7 (

**Ans :**C)19. If the total investment in district B shows the same rate of increase in 1997, as it had shown from 1995 to 1996, what approximately would be the total investment in B in 1997?

(A) Rs. 9,170 crore (B) Rs. 8,540 crore (C) Rs. 9,850 crore (D) Rs. 10,020 crore (

**Ans :**C)20. A man sells an article t 5% above the cost price. If he had bought it at 5% less than what he paid for it and sold it for Rs. 2 less, he would have gained 10%. The cost price of the article is–

(A) Rs. 250 (B) Rs. 400 (C) Rs. 200 (D) Rs. 350 (

**Ans :**B)21. The radii of the base of a cylinder and a cone are equal and their volumes are also equal. Then the ratio of their heights is–

(A) 1 : 4 (B) 2 : 1 (C) 1 : 2 (D) 1 : 3 (

**Ans :**D)22. If a person spends 40% of his income on food, 20% on house rent and 70% of the remaining on children's education, then the percentage of his income left is–

(A) 8% (B) 10% (C) 12% (D) 6% (

**Ans :**C)23. If tan θ + sec θ = 2, then the value of tan θ is–

(A) 2/3 (B) 3/5 (C) 3/4 (D) 4/5 (

**Ans :**C)24. Let

*a*be a positive integer. When 89 and 125 are divided by*a*, the remainders are 4 and 6 respectively. Then the value of*a*is–(A) 15 (B) 17 (C) 9 (D) 7 (

**Ans :**B)25. Points A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction, They meet in 5 hours. If the cars travel towards each other, they meet in 1 hour. What is the speed of the faster car?

(A) 80 km/hour (B) 40 km/hour (C) 70 km/hour (D) 60 km/hour (

**Ans :**D)26. A cylindrical rod of radius 30 cm and length 40 cm is melted and made into spherical balls of radius 1 cm. The number of spherical balls is–

(A) 40000 (B) 27000 (C) 36000 (D) 90000 (

**Ans :**B)27. A merchant purchases a wrist watch for Rs. 1,200 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. The list price of the watch is–

(A) Rs. 1,400 (B) Rs. 1,600 (C) Rs. 1,800 (D) Rs. 1,200 (

**Ans :**B)28. The sum of two numbers is 15⅓ and their difference is 4⅔. The product of the numbers is–

(A) 53 ⅓ (B) 60 (C) 48⅔ (D) 50 (

**Ans :**A)29. A and B can separately finish a piece of work in 20 days and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work is–

(A) 40 days (B) 60 days (C) 30 days (D) 50 days (

**Ans :**A)30. The ratio of the radii of two cylinders is 2 : 1 and their heights are in the ratio 3 : 2. Then their volumes are in the ratio–

(A) 6 : 1 (B) 4 : 3 (C) 6 : 5 (D) 3 : 1 (

**Ans :**A)