A bucket contains liquid A and B in the ratio 11:12. 92 litres of the mixture is taken out and filled with 92 litres of B. Now the ratio changes to 9:10. Find the quantity of liquid B initially. (In litres)
Ratio of A : B = 11 : 12
Let total mixture = 23x
A = 11x
B = 12x
92 litres mixture removed
A removed = (11/23) × 92 = 44
B removed = (12/23) × 92 = 48
Remaining:
A = 11x − 44
B = 12x − 48
92 litres of B added
New B = 12x − 48 + 92
= 12x + 44
New ratio = 9 : 10
(11x − 44) / (12x + 44) = 9 / 10
10(11x − 44) = 9(12x + 44)
110x − 440 = 108x + 396
2x = 836
x = 418
Initial quantity of B
= 12x
= 12 × 418
= 5016 litres
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