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A Can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drained off and the Can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the Can initially ?
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- 10 litres
- 20 litres
- 21 litres
- 25 litres
Correct Option: C
Let the original quantity be 12x litres.
In 9 litres of the mixture,
| Liquid A = | × 9 = | litres | ||
| 12 | 4 |
| Liquid B = | × 9 = | litres | ||
| 12 | 4 |
According to question,
| = | 7x − | = 7/9 | ||
| 4 | ||||
| 5x − | + 9 | |||
| 4 | ||||
| ⇒ | = | ||
| 20x − 15 + 36 | 9 |
| ⇒ | = | ||
| 20x + 21 | 9 |
| ⇒ | = | ||
| 20x + 21 | 9 |
⇒ 36x – 27 = 20x + 21
⇒ 36x – 20x = 21 + 27
⇒ 16x = 48
⇒ x = 3
Original quantity of liquid A
= 7x = 7 × 3 = 21 litres
