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- Question
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
- Correct Answer
- 2 : 3 : 4
ExplanationOriginally, 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.
Ratio and Proportion problems
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- 1. 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.
- 2. 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 - 3. 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 - 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 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.
- 6. 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.
- 7. 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 - 8. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Options- A. 2 : 5
- B. 3 : 5
- C. 4 : 5
- D. 6 : 7 Discuss
Correct Answer: 4 : 5
Explanation:
Let the third number be x.Then, first number = 120% of x = 120x = 6x 100 5 Second number = 150% of x = 150x = 3x 100 2 ∴ Ratio of first two numbers = ❨ 6x : 3x ❩ = 12x : 15x = 4 : 5. 5 2 - 9. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
Options- A. 3 : 3 : 10
- B. 10 : 11 : 20
- C. 23 : 33 : 60
- D. Cannot be determined Discuss
Correct Answer: 23 : 33 : 60
Explanation:
Let A = 2k, B = 3k and C = 5k.A's new salary = 115 of 2k = ❨ 115 x 2k ❩ = 23k 100 100 10 B's new salary = 110 of 3k = ❨ 110 x 3k ❩ = 33k 100 100 10 C's new salary = 120 of 5k = ❨ 120 x 5k ❩ = 6k 100 100 ∴ New ratio ❨ 23k : 33k : 6k ❩ = 23 : 33 : 60 10 10 - 10. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Options- A. 20 litres
- B. 30 litres
- C. 40 litres
- D. 60 litres Discuss
Correct Answer: 60 litres
Explanation:
Quantity of milk = ❨ 60 x 2 ❩litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = ❨ 40 ❩ . 20 + x Now, ❨ 40 ❩ = 1 20 + x 2 ⟹ 20 + x = 80
⟹ x = 60.
∴ Quantity of water to be added = 60 litres.
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