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
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