A tank contains liquid A and B in the ratio 13:12. 50 litres of the mixture are taken out and filled with 50 litres of B. Now the ratio changes to 7:8. Find the quantity of liquid B initially.
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Correct answer: D
Explanation
Given:
Liquid A : B = 13 : 12
50 liters of mixture taken out
50 liters of liquid B added
New ratio = 7 : 8
Let the total mixture = 25x
A = 13x
B = 12x
50 liters of mixture taken out
A = (13/25) × 50 = 26
B = (12/25) × 50 = 24
Now the remaining
A = 13x − 26
B = 12x − 24
Now 50 liters of B added
B = 12x − 24 + 50 = 12x + 26
Now the new ratio
(13x − 26) : (12x + 26) = 7 : 8
8(13x − 26) = 7(12x + 26) 26)
104x − 208 = 84x + 182
20x = 390
x = 19.5
Now initial B = 12x = 12 × 19.5 = 234 liters