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- Question
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
- Correct Answer
- 5 : 3
ExplanationLet 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.
Ratio and Proportion problems
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- 1. 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 - 2. 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 - 3. √1.5625 =?
Options- A. 1.05
- B. 1.25
- C. 1.45
- D. 1.55 Discuss
Correct Answer: 1.25
Explanation:
1|1.5625( 1.25 |1 |------- 22| 56 | 44 |------- 245| 1225 | 1225 |------- | X |-------∴ √1.5625 = 1.25.- 4. If a = 0.1039, then the value of √4a2 - 4a + 1 + 3a is:
Options- A. 0.1039
- B. 0.2078
- C. 1.1039
- D. 2.1039 Discuss
Correct Answer: 1.1039
Explanation:
√4a2 - 4a + 1 + 3a = √(1)2 + (2a)2 - 2 x 1 x 2a + 3a= √(1 - 2a)2 + 3a
= (1 - 2a) + 3a
= (1 + a)
= (1 + 0.1039)
= 1.1039
- 5. If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5?
Options- A. 13.41
- B. 20.46
- C. 21.66
- D. 22.35 Discuss
Correct Answer: 22.35
Explanation:
3√5 + √125 = 17.88⟹ 3√5 + √25 x 5 = 17.88
⟹ 3√5 + 5√5 = 17.88
⟹ 8√5 = 17.88
⟹ √5 = 2.235
∴ √80 + 6√5 = √16 x 5 + 6√5
= 4√5 + 6√5
= 10√5 = (10 x 2.235) = 22.35
- 6. 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.
- 7. 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 - 8. 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 - 9. 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.
- 10. 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.
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