Type – 1 (Continued Proportion)

1. What is the fourth proportional to 189, 273 and 153? (CGL Mains 2017)

1. 117 
2. 299 
3. 221 
4. 187

Option :- 3

2. Find two numbers such that their mean proportional is 18 and the third proportional to them is 144. (CGL Mains 2017)

1. 6 and 42 
2. 9 and 36 
3. 3 and 18 
4. 6 and 12

3. What is the ratio of the third proportional to 0.4 and 0.8, to the mean proportional between 13.5 and 0.24? (CGL Mains 2018)

1. 5 : 4 
2. 7 : 8 
3. 8 : 9 
4. 9 :10

4. What is the sum of the mean proportional between 10.8 and 4.8 and the third proportional of 2 and 4?  (CPO 2018)

1. 10.2 
2. 11.2 
3. 8.2 
4. 15.2

5. What is the ratio of the mean proportional between 8.1 and 3.6 and the third proportional of 2 and 3? (CPO 2018)

1. 5:6 
2. 5:4 
3. 4:5 
4. 6:5

6. If x is subtracted from each of the numbers 20, 37, 54 and 105, then the numbers so obtained in this order are in proportion. What is the mean proportional between (7x-5) and (x + 1)? (CPO 2019)

1. 8 
2. 6 
3. 12 
4. 9

7. What number should be added to each of the numbers 55, 100, 65 and 116 so that the resulting numbers are in continued proportion? (CGL 2017)

1. 20 
2. 10 
3. 5 
4. 15

8. What number should be added to each of the numbers 94, 24, 100 and 26, so that the resulting numbers are in continued proportion? (CGL 2017)

1. 10 
2. 11 
3. 9 
4. 8

9. What number should be added to each of the numbers 103, 135, 110 and 144 so that the resulting numbers are in proportion? (CGL Mains 2017)

1. 12 
2. 15 
3. 9 
4. 6

10. If x is subtracted from each of 23, 39, 32 and 56, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 4) and (3x + 1)? (CGL 2018)

1. 15 
2. 14 
3. 12 
4. 10

11. If x is added to each of 12, 28, 21 and 45, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 3) and (4x + 1)? (CGL 2018)

1. 15 
2. 18 
3. 12 
4. 10

12. When x is subtracted from each of 21, 22, 60 and 64, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 1) and (7x + 8)?  (CGL 2018)

1. 21 
2. 24 
3. 27 
4. 18

13. What is the ratio of the mean proportional between 4.8 and 10.8 and the third proportional to 0.4 and 2.4? (CGL 2018)

1. 1 : 2 
2. 2 : 1 
3. 3 : 2 
4. 2 : 3

14. When x is added to each of 2, 3, 30 and 35, then the numbers obtained in this order, are in proportion. What is the mean proportional between (x+7) and (x-2)? (CGL Mains 2018)

1. 7 
2. 4 
3. 6 
4. 5

15. If x is the mean proportional between 12.8 and 64.8 and y is the third proportional to 38.4 and 57.6, then 2x : y is equal to: (CGL 2019)

1. 2 : 3 
2. 1 : 2 
3. 3 : 4 
4. 4 : 5

16. If 2x+1, x+2, 2 and 5 are in proportion, then what is the mean proportional between 3.5(1-x) and 8(1+x)? (CGL 2019)

1. 5.5 
2. 4.25 
3. 5.25 
4. 4.5

17. What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportion between the number (x+1) and (3x+1)? (CGL 2019)

1. 12 
2. 9 
3. 15 
4. 10

18. When x is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x – 2) and (5x + 4)? 

1. 35 
2. 20 
3. 30 
4. 42

19. If a : b = b : c, then a^4 : b^4 is equal to: (SSC CGL 2005)

1. ac : b^2
2. a^2 : c^2
3. c^2 : a^2
4. b^2 : ac

20. If b is the mean proportional of a and c, then (a – b)^3 : (b – c)^3 equals to :

1. a^3 : c^3
2. b^2 : c^2
3. a^2 : c ^2
4. a ^3 : b^3

Option :- 4

Type -2 (Simplification)

21. The compound ratio of the inverse relations of the ratios x : yz, y : zx, z : xy is: (SSC CGL Pre 2016)

1. 1 : xyz
2. xyz : 1
3. 1 : 1
4. x : yz

22. If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns + ou) is equal to:

1. 1 : 3
2. 1 : 2
3. 2 : 3
4. 3 : 2

23. If a : b = c : d, then (ma +nc) : (mb + nd) is equal to: (SSC CGL 2007)

1. a : b
2. c : d
3. (a + c) : (b + d)
4. (c – a) : (b – d)

Option :- 2

24. If (5a – 3b) : (4a – 2b) = 2 : 3, then a : b is equal to: (CGL 2018)

1. 5 : 8 
2. 5 : 7 
3. 2 : 3 
4. 3 : 4

25. If a : b = 3 : √5, then find the value of (2a + b) : (3a – 2b). (CHSL 2018)

1. (64 + 21√5 ) / 64 
2. (64 + 21√5) / 62
3. (64 + 21√5 ) / 63
4. (64 + 21√5) / 61

26. If (5x+2y) : (10x + 3y) = 5 : 9, then (2x^2 + 3y^2 ) : (4x^2 + 9y^2 ) = ? (CGL Mains 2018)

1. 31 : 87 
2. 10 : 27 
3. 16 : 47 
4. 1 : 3

27. If (10a^3 + 4 b³) : (11a^3 – 15b^3 ) = 7 : 5, then (3a + 5b) : (9a – 2b) =? (SSC CGL Mains 2019)

1. 10:13 
2. 5:4 
3. 3:2 
4. 8:7

28. If 2/3 of A = 75% of B = 0.6% of C, then A : B : C, then A : B : C is: (SSC CGL 2008)

1. 2 : 3 :3
2. 3 : 4 :5
3. 4 : 5 : 6
4. 9 : 8 : 10

Option :- 4

29. If 12A = 16B = 15C; find A:B:C. (CGL Mains 2017)

1. 12:16:15 
2. 15:16:12 
3. 20:15:16 
4. 16:15:20

30.If (4/5)A = 3B = (2/3)C, then what is A: B: C? (SSC CHSL 2018)

1. 12 : 3 : 16
2. 12 : 45 : 10
3. 15 : 4 : 18
4. 9 : 12 : 16

31. If X : Y : Z = 3 : 4 : 5, then what will be the ratio of (X/Y) : (Y/Z): (Z/X)? (SSC CHSL 2018)

1. 5 : 4 : 3
2. 30 : 40 : 27
3. 45 : 48 : 100
4. 20 : 15 : 12

(B) u^2 : w^2 

(C) u^2 v : w^3 

(D) u : w32. If a : b : c = 1/4 : 1/3 : 1/2 then a/b : b/c : c/a =?  

1. 12:9:8 
2. 8:9:24 
3. 9:8:24 
4. 9:12:8

32. If (a+b) : (b+c) : (c+a) = 7:6:5 and a+b+c = 27, then what will be the value of 1/a : 1/b : 1/c? (CGL Mains 2018)

1. 3:6:4 
2. 3:2:4 
3. 4:3:6 
4. 3:4:2

30. A, B and Care partners. They share profits in the ratio of 5:3:6. If A earns Rs.1,92,380 as his share of profit, then the share of C is: (CGL 2018)

1. Rs.2,30,856 
2. Rs.1,15,428 
3. Rs.82,449 
4. Rs.1,60,317

31. Rs. 4,06,736 is divided among A, B and C such that the ratio between A and B is 2 : 3 and B and C is 1 : 2. The share of C is : (CGL 2018)

1. Rs.73, 952 
2. Rs.1,10,928 
3. Rs.2,64,796 
4. Rs.2,21,856

32. A sum of Rs.12,000 is divided between A, B, C and D such that the ratio of shares of A and B is 8:9, that of B and C is 2:3 and that of C and D is 9: 13. What is the difference between the shares of B and D? (CGL 2019)

1. Rs.1,320 
2. Rs.2,400 
3. Rs.2,520 
4. Rs.2,760

 A sum of ₹ 4,360 was to be divided among A, B, C and D in the ratio of 3 : 4 : 5 : 8, but it was divided in the ratio of 1/3 : 1/4 : 1/5 : 1/8 by mistake. As a result: (SSC CHSL 2019)

1. A received ₹ 956 more 
2. B received ₹ 318 more 
3. D received ₹ 1,144 less 
4. C received ₹ 132 less

33. A man has 3 sons, 2 daughters and a wife. They divided a sum of Rs 19000 among themselves such that each daughter got 1.5 times the amount received by each son and his wife received 600 less than each son. What is the total amount (in Rs) received by the 3 sons together? (CGL 2017)

1. 2800 
2. 3600 
3. 5600 
4. 8400

84.A sum of Rs. 2489 is divided among A, B and C such that if Rs. 12, Rs. 12 and Rs. 5 be diminish from the shares of A, B and C respectively, then their shares will be in the ratio of 5: 3: 4. What is the new share (in Rs.) of C? (SSC CHSL 2018)

1. 750
2. 1060
3. 1475
4. 820

85.The ratio of two positive numbers is 3 : 7. If their product is 1344, then what is the sum of both the numbers? (SSC CHSL 2018)

1. 80
2. 60
3. 30
4. 168

34. Rs 60500 is divided among A, B and C such that A receives 2/9 as much as B and C together and B receives 3/7 of as much as A and C together. What is the share of C (in Rs)? (CGL 2017)

1. 29850 
2. 30120 
3. 31350 
4. 37250

35. Rs. 11,550 has to be divided between X, Y & Z such that X gets 4/5 of what Y gets and Y gets 2/3 of what Z gets. How much more does Z get over X (in Rs)? (CGL 2017)

1. 7200 
2. 1800 
3. 13* 9 
4. 2450

36. If Rs 25,000 is to be divided between A, B and C in the ratio 1/10 : 1/6 : 1/15, then how much will C get (in Rs)?(CGL Mains 2017) 

1. 5000 
2. 7500 
3. 10000 
4. 12500

37. A company, at the time of inflation reduced the staff in the ratio 5: 3 and average salary per employee is increased in the ratio 7 : 8. By doing so, the company saved Rs 55000. What was the initial expenditure (in Rs) of company? (CGL 2017)

1. 155000 
2. 160000 
3. 175000 
4. 215000

38. The entry ticket at a fun park was increased in the ratio 7 : 9, due to which footfalls fell in the ratio 13 : 11. What is the new daily collection (in Rs), if the daily collection before the price hike was Rs 2,27,500? (CGL Mains 2017)

1. 237500 
2. 247500 
3. 232500 
4. 242500

39. If by increasing the price of a ticket in the ratio 8:11 the number of tickets sold fall in the ratio 23:21 then what is the increase (in Rs) in revenue if revenue before increase in price of ticket was Rs 36,800? (CGL Mains 2017)

1. 21250 
2. 9400 
3. 7850 
4. 12850

40. The ratio of number of cans of orange, pineapple and mixed fruit juices kept in a store is 8: 9: 15. If the store sells 25%, 33.33% and 20% of orange, pineapple and mixed fruit juices cans respectively, then what is the ratio of number of cans of these juices in the remaining stock? (CGL 2017)

1. 1 : 1 : 2 
2. 6 : 6 : 13 
3. 12 : 15 : 19 
4. 4 : 9 : 13

41. There are 50 paisa, 25 paisa and Rs.1 coins in a bag in the ratio 5:8:1. If the total value of all the coins is Rs. 55, how many 25 paisa coins are there in the bag? (CGL 2018)

1. 25 
2. 50 
3. 80 
4. 10

42. A bag has Rs 43 in the form of 5 rupee, 50-paise and 10-paise coins in the ratio of 1:5:11. What is the total number of 50-paise coins? (CGL 2017)

1. 5 
2. 25 
3. 55 
4. 50

43. A bag has Rs.51.25 in the form of 2 rupee, 50-paise and 25-paise coins in the ratio of 3:5:7. What is the total number of 50-paise coins? (CGL 2017)

1. 15 
2. 35 
3. 25 
4. 5

44. A purse has Rs 34.5 in the form of 1 rupee, 50-paise and 10-paise coins in the ratio of 6:9:10. Find the number of 10-paise coins. (CGL Mains 2017)

1. 10 
2. 30 
3. 20 
4. 40

45. Price of a diamond is directly proportional to square of its weight. A man broke the diamond accidently in three pieces in the ratio of 3 : 5 : 7 and thus loses Rs 42600. What was the original price (in Rs) of the diamond? (CGL 2017)

1. 11786 
2. 60000 
3. 67500 
4. 75000

Type -4