Ratio and Proportion problems
- 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:
| 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 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:
| 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 |
- 3. 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.
- 4. 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 |
- 5. 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:
| Then, | 3x - 9 | = | 12 |
| 5x - 9 | 23 |
⟹ 23(3x - 9) = 12(5x - 9)
⟹ 9x = 99
⟹ x = 11.
∴ The smaller number = (3 x 11) = 33.
- 6. Total number of students in a class is 95. if the total number of girls in the class is 45, then the ratio of total number if boys to total number girls is
Options- A. 9:10
- B. 7:8
- C. 10:9
- D. 9:11 Discuss
Correct Answer: 10:9
Explanation:
Let the total number of boys in the class be x.
Then, according to the question,
x + 45 = 95
x = 95 - 45 = 50
Hence, the required ratio of total number of boys to total number of girls = B:G = 50:45 = 10:9
- 7. The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 490, Krishan has?
Options- A. Rs. 2890
- B. Rs. 2330
- C. Rs. 1190
- D. Rs. 2680 Discuss
Correct Answer: Rs. 2890
Explanation:
Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
? Ram : Gopal : Krishan = 49 : 119 : 289
? Ram : Krishan = 49 : 289
Thus, 49 : 289 = 490 : N
&there N = 289 x 490 / 49
= Rs. 2890
- 8. The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs. 6000 more than the television set, the price of the television set is?
Options- A. Rs. 6000
- B. Rs. 10000
- C. Rs. 12000
- D. Rs. 18000 Discuss
Correct Answer: Rs. 12000
Explanation:
Let the price of a scooter be Rs. 3x and that of a television set Rs. 2x.
Then, 3x - 2x = 6000
? x = 6000
? Cost of a television set = 2x
= Rs. 12000
- 9. If 8 : y = y : 18 , then y is equal to?
Options- A. 144
- B. 72
- C. 26
- D. 12 Discuss
Correct Answer: 12
Explanation:
? 18 x 18 = y2
? y = ?144 = 12
- 10. A circle and a square have same area. Therefore, the ratio of the side of the square and the radius of the circle is?
Options- A. ?? : 1
- B. 1 : ??
- C. 1 : ?
- D. ? : 1 Discuss
Correct Answer: ?? : 1
Explanation:
Let the side of the square be 'a' and let the radius of the circle be 'r'
Then, a2 = ?r2
? a2 / r2 = ?
? a / r = ??
? a : r = ?? : 1
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