The milk and water in two vessels P and Q are in the ratio 5 : 2 and 2 : 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel R containing half milk and half water?
Explanation:
Let the amount of P and Q mixed be p and q liters respectively.
Total amount of milk obtained by mixing P and Q = 5/7 × p + 2/5 × q Total amount of water obtained by mixing P and Q = 2/7 × p + 3/5 × q
We want the mixture to have half milk and half water i.e., quantity of milk and water should be same in the final mixture.
⇒ 5/7 × p + 2/5 × q = 2/7 × p + 3/5 × q
⇒ 5/7 × p - 2/7 × p = 3/5 × q - 2/5 × q
⇒ 3/7 × p = 1/5 × q
⇒ p/q = 7/15
Hence, option (b).
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