Ratio and Proportion problems
- 1. The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Options- A. 20
- B. 30
- C. 48
- D. 58 Discuss
Correct Answer: 30
Explanation:
Let the three parts be A, B, C. Then,
| A : B = 2 : 3 and B : C = 5 : 8 = | ❨ | 5 x | 3 | ❩ | : | ❨ | 8 x | 3 | ❩ | = 3 : | 24 |
| 5 | 5 | 5 |
| ⟹ A : B : C = 2 : 3 : | 24 | = 10 : 15 : 24 |
| 5 |
| ⟹ B = | ❨ | 98 x | 15 | ❩ | = 30. |
| 49 |
- 2. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Options- A. 8 : 9
- B. 17 : 18
- C. 21 : 22
- D. Cannot be determined Discuss
Correct Answer: 21 : 22
Explanation:
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
| ⟹ | ❨ | 120 | x 7x | ❩ | and | ❨ | 110 | x 8x | ❩ |
| 100 | 100 |
| ⟹ | 42x | and | 44x |
| 5 | 5 |
| ∴ The required ratio = | ❨ | 42x | : | 44x | ❩ | = 21 : 22. |
| 5 | 5 |
- 3. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Options- A. 2 : 5
- B. 3 : 7
- C. 5 : 3
- D. 7 : 3 Discuss
Correct Answer: 5 : 3
Explanation:
| Let 40% of A = | 2 | B |
| 3 |
| Then, | 40A | = | 2B |
| 100 | 3 |
| ⟹ | 2A | = | 2B |
| 5 | 3 |
| ⟹ | A | = | ❨ | 2 | x | 5 | ❩ | = | 5 |
| B | 3 | 2 | 3 |
∴ A : B = 5 : 3.
- 4. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
Options- A. Rs. 17,000
- B. Rs. 20,000
- C. Rs. 25,500
- D. Rs. 38,000 Discuss
Correct Answer: Rs. 38,000
Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
| Then, | 2x + 4000 | = | 40 |
| 3x + 4000 | 57 |
⟹ 57(2x + 4000) = 40(3x + 4000)
⟹ 6x = 68,000
⟹ 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
- 5. If Rs. 782 be divided into three parts, proportional to ½ : ⅔ : ¾, then the first part is:
Options- A. Rs. 182
- B. Rs. 190
- C. Rs. 196
- D. Rs. 204 Discuss
Correct Answer: Rs. 204
Explanation:
Given ratio = ½ : ⅔ : ¾ = 6 : 8 : 9.
| ∴ 1st part = Rs. | ❨ | 782 x | 6 | ❩ | = Rs. 204 |
| 23 |
- 6. A and B together have Rs. 1210. If 4⁄15 of A's amount is equal to ⅖ of B's amount, how much amount does B have?
Options- A. Rs. 460
- B. Rs. 484
- C. Rs. 550
- D. Rs. 664 Discuss
Correct Answer: Rs. 484
Explanation:
| 4 | A | = | 2 | B | |
| 15 | 5 |
| ⟹ A = | ❨ | 2 | x | 15 | ❩B |
| 5 | 4 |
| ⟹ A = | 3 | B |
| 2 |
| ⟹ | A | = | 3 |
| B | 2 |
⟹ A : B = 3 : 2.
| ∴ B's share = Rs. | ❨ | 1210 x | 2 | ❩ | = Rs. 484. |
| 5 |
- 7. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
Options- A. 50
- B. 100
- C. 150
- D. 200 Discuss
Correct Answer: 150
Explanation:
Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
| Then, sum of their values = Rs. | ❨ | 25x | + | 10 x 2x | + | 5 x 3x | ❩ | = Rs. | 60x |
| 100 | 100 | 100 | 100 |
| ∴ | 60x | = 30 | ⟺ x = | 30 x 100 | = 50. |
| 100 | 60 |
Hence, the number of 5 p coins = (3 x 50) = 150.
- 8. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Options- A. 2 : 3 : 4
- B. 6 : 7 : 8
- C. 6 : 8 : 9
- D. None of these Discuss
Correct Answer: 2 : 3 : 4
Explanation:
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
| ⟹ | ❨ | 140 | x 5x | ❩ | , | ❨ | 150 | x 7x | ❩ | and | ❨ | 175 | x 8x | ❩ |
| 100 | 100 | 100 |
| ⟹ 7x, | 21x | and 14x. |
| 2 |
| ∴ The required ratio = 7x : | 21x | : 14x |
| 2 |
⟹ 14x : 21x : 28x
⟹ 2 : 3 : 4.
- 9. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Options- A. Rs. 500
- B. Rs. 1500
- C. Rs. 2000
- D. None of these Discuss
Correct Answer: Rs. 2000
Explanation:
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
⟹ x = 1000.
∴ B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
- 10. The fourth proportional to 5, 8, 15 is:
Options- A. 18
- B. 24
- C. 19
- D. 20 Discuss
Correct Answer: 24
Explanation:
Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
⟹ 5x = (8 x 15)
| x = | (8 x 15) | = 24. |
| 5 |
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