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### Question

A mixture of milk and water contains 29 parts of milk and 14 parts of water. How much fraction of the mixture should be removed and replaced by water so that ratio of water and milk becomes equal?

**A**

${15/58}$.

**B**

$1{16/57}$.

**C**

$2{11/60}$.

**D**

$3{3/20}$.

**Soln.**

**Ans: a**

Let the volume of the mixture be 29 + 14 = 43 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $14 - {14x}/43 + x$. The volume of the milk in the new mixture would be $29 - {29x}/43.$ Equating the two volumes and solving for x we get x = ${43 × 15}/{2 × 29}$. The fraction that must be removed = $1/43$ × ${43 × 15}/{2 × 29}$, which gives $15/{2 × 29}$ = ${15/58}$.