Question

A juice vendor mixes water with pure orange juice. If he sells the mixture at the cost price of pure orange juice and makes a profit of 20%, what is the ratio of water to pure orange juice in the mixture, respectively?

• A. 1 : 4
• B. 1 : 5
• C. 4 : 1
• D. 5 : 1

Answer 1

Answer:

B. 1 : 5

Let the cost price of pure orange juice be ₹100 per liter.

He sells the mixture at the same price, ₹100 per liter, and gains (20%).

So, the actual cost of 1 liter of mixture is:

$\frac{100 \times 100}{120} = 83\frac{1}{3}$

Thus, in 1 liter mixture:

• Cost of orange juice = ₹83$(\frac{1}{3})$

• Water is free.

So orange juice fraction:

$\frac{83\frac{1}{3}}{100}=\frac{5}{6}$

Therefore water fraction:

$1-\frac{5}{6}=\frac{1}{6}$

Hence, the ratio of water : orange juice is

$\frac{1}{6} : \frac{5}{6} = 1:5$

So, the required ratio is:

$\boxed{1:5}$