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Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, then they are in the ratio 12 : 23. Find the smaller number.
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- 27
- 33
- 49
- 55
Correct Option: B
Let the numbers be 3x and 5x.
| ∴ | = | ||
| 5x − 9 | 23 |
⇒ 69x – 60x = 207 – 108
| ⇒ x = | = 11 | |
| 9 |
∴ The smaller number
= 3x = 33
Second Method :
Here, a = 3, b = 5, x= 9, c = 12, d = 23
| 1st Number = | |
| ad − bc |
| = | |
| 3 × 23 − 5 × 12 |
| = | |
| 69 − 60 |
| = | = 33 | |
| 9 |
| 2nd Number= | |
| ad − bc |
| = | |
| 3 × 23 − 5 × 12 |
| = | |
| 69 − 60 |
| = | = 55 | |
| 9 |
∴ Smallest number = 33
