Question
A cistern A has 270 litres of a milk–water mixture in
the ratio 6:x. If 56 litres are withdrawn and mixed with 8 litres of water in another vessel B, the resulting milk to water ratio becomes 7:5. What was the initial milk quantity in A?Solution
Milk in 56 litres = (6/(6+x)) × 56 = 336/(6+x) litres Water in 56 litres = (x/(6+x)) × 56 = 56x/(6+x) litres Water in B after addition = 56x/(6+x) + 8 Given: 336/(6+x) : [56x/(6+x) + 8] = 7:5 336/(6+x) = (392x/(5(6+x))) + 56/5 Multiply both sides: 1680 = 392x + 336 + 56x 1680 – 336 = 448x → 1344 = 448x → x = 3 Initial milk = (6/9) × 270 = 180 litres.
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