80 litres of a mixture of spirit and water in the ratio 7 : 9 is present in a container A. 20 litres of the mixture is transferred to another container B. Then the container A is filled with 20 litres of water. Then 32 litres of the mixture is again transferred to container B. The ratio of water to spirit of the mixture in container B is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 131 : 77.
Total amount of mixture in container A = 80 litres
Ratio of spirit and water in container A = 7 : 9
Let the common ratio be x.
According to the question -
⇒ 7x + 9x = 80
⇒ 16x = 80
⇒ x = 5
Initial quantity of spirit in container A = 7x = 7 × 5 = 35 lt
Initial quantity of water in container A = 9x = 9 × 5 = 45 lt
When 20 litres of the mixture is transferred to container B -
⇒ The quantity of spirit transferred = 20 × 7/16 = 35/4 litres
⇒ The quantity of water transferred = 20 × 9/16 = 45/4 litres
After filling container A with 20 litres of water -
⇒ The quantity of water in container A = 45 - 45/4 + 20 = 215/4 litres
⇒ The quantity of spirit in container A= 35 - 35/4 = 105/4 litres
Ratio of spirit and ater in new mixture = (105/4) : (215/4) = 21 : 43
Transferring 32 litres of mixture to container B -
⇒ The quantity of spirit transferred = 32 × 21/64 = 21/2 litres
⇒ The quantity of water transferred = 32 × 43/64 = 43/2 litres
Amount of spirit in container B = 35/4 + 21/2 = 77/2
Amount of water in container B = 45/4 + 43/2 = 131/2
The ratio of water to spirit of the mixture in container B = (131/2) : (77/2) = 131 : 77