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A receptacle is filled with a mixture of two liquids L1 and L2 in the ratio of 7 : 5. Due to poor handling, 9 litres of mixture fell from the receptacle and the volume was made up with L2, thus the ratio of the both liquids in the mixture becomes 7 : 9. Find the initial quantity of L1 in the mixture.

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A receptacle is filled with a mixture of two liquids L1 and L2 in the ratio of 7 : 5. Due to poor handling, 9 litres of mixture fell from the receptacle and the volume was made up with L2, thus the ratio of the both liquids in the mixture becomes 7 : 9. Find the initial quantity of L1 in the mixture.
1). 24 litres
2). 21 litres
3). 26 litres
4). 28 litres


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Answered by on | Votes 1 |

Let the receptacle initially contains 7x and 5x of mixtures L1 and L2 respectively.

Remaining quantity of L1,

= (7x – 7 × 9/12)

= (7x - 21/4) litres

Remaining quantity of L2,

= (5x – 5 × 9/12)

= (5x - 15/4) litres

According to the question,

[(7x - 21/4)/ (5x - 15/4) + 9] = 7/9

⇒ (28x - 21)/ (20x + 21) = 7/9

⇒ 252x - 189 = 140x + 147 ⇒ 112x = 336

⇒ x = 3

∴ Initial quantity of L1 in the mixture = 7 × 3 = 21 litres

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