Question
A tank A holds 320 litres of a milk–water mixture in
the ratio 13:x. If 50 litres are transferred from A to B and then 15 litres of water are added to B, the milk to water ratio in B becomes 5:3. Find the initial quantity of milk in A.Solution
Milk in 50 litres = (13/(13+x)) × 50 = 650/(13+x) litres Water in 50 litres = (x/(13+x)) × 50 = 50x/(13+x) litres Water in B after addition = 50x/(13+x) + 15 Given: 650/(13+x) : [50x/(13+x) + 15] = 5:3 650/(13+x) = (250x/(3(13+x))) + 25 650 = (250x/3) + 325 + 25x 325 = (325x/3) → x = 3 Initial milk = (13/16) × 320 = 260 litres.
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