Question

A dishonest milkman sells milk at cost price but he mixes water and earns \[14\left( \dfrac{2}{7} \right)%\]. Find the ratio of mixture and milk in the mixture?

Answer 1

Hint: Take the ratio of milk to water as x : 1. Similarly, the ratio of mixture to milk is x+1 : 1. Find the value of x and get the ratio of the mixture to milk.

Complete step by step answer:
Let us consider the cost price of the milk as C.
Let the ratio of milk to water be x : 1.
It is said that the dishonest milkman sells milk at the cost price but he mixes water and earns \[14\left( \dfrac{2}{7} \right)%\].
Thus according to the question we can write that,
\[{{C}_{x}}=C\times \dfrac{14+\dfrac{2}{7}}{100}\]
Thus we got the expression, \[{{C}_{x}}=C\left( \dfrac{14+\dfrac{2}{7}}{100} \right)\].
Let us cancel out C from LHS and RHS. Thus find the value of x.
\[\begin{align}
  & x=\left( 14+\dfrac{2}{7} \right)\times \dfrac{1}{100} \\
 & x=\left( \dfrac{14\times 7+2}{7} \right)\times \dfrac{1}{100}=\dfrac{100}{7}\times \dfrac{1}{100}=\dfrac{1}{7} \\
\end{align}\]
Thus we got the milk to water ratio as 7 : 1.
Thus the mixture to milk ratio = x + 1 : 1 = 7 + 1 : 7 = 8 :7.
Thus we got the mixture to milk ratio = 8 : 7.

Note: The Mixture contains both milk and water. The milk and water is in the ratio x : 1. Thus in mixture it will be (x + 1). Thus the ratio of mixture to milk will be x + 1 : x. \[14\left( \dfrac{2}{7} \right)\] can also be solved as \[\left( 14\times 7 \right)+2=100\], according to the division, (quotient \[\times \] divisor) + remainder.