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- Question
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
- Correct Answer
- 23 : 33 : 60
ExplanationLet 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
Ratio and Proportion problems
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- 1. 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 - 2. 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 - 3. 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.
- 4. 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.
- 5. 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.
- 6. 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.
- 7. If 0.75 : x :: 5 : 8, then x is equal to:
Options- A. 1.12
- B. 1.2
- C. 1.25
- D. 1.30 Discuss
Correct Answer: 1.2
Explanation:
(x x 5) = (0.75 x 8) ⟹ x = ❨ 6 ❩ = 1.20 5 - 8. Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
Options- A. 27
- B. 33
- C. 49
- D. 55 Discuss
Correct Answer: 33
Explanation:
Let the numbers be 3x and 5x.Then, 3x - 9 = 12 5x - 9 23 ⟹ 23(3x - 9) = 12(5x - 9)
⟹ 9x = 99
⟹ x = 11.
∴ The smaller number = (3 x 11) = 33.
- 9. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options- A. 20 hours
- B. 25 hours
- C. 35 hours
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 35 hours
Explanation:
Suppose pipe A alone takes x hours to fill the tank.Then, pipes B and C will take x and x hours respectively to fill the tank. 2 4 ∴ 1 + 2 + 4 = 1 x x x 5 ⟹ 7 = 1 x 5 ⟹ x = 35 hrs.
- 10. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
Options- A. 1 hour
- B. 2 hours
- C. 6 hours
- D. 8 hours Discuss
Correct Answer: 6 hours
Explanation:
Let the cistern be filled by pipe A alone in x hours.Then, pipe B will fill it in (x + 6) hours.
∴ 1 + 1 = 1 x (x + 6) 4 ⟹ x + 6 + x = 1 x(x + 6) 4 ⟹ x2 - 2x - 24 = 0
⟹ (x -6)(x + 4) = 0
⟹ x = 6. [neglecting the negative value of x]
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