Arithmetic

Mixture & Alligation

Medium

applied

If water is mixed with milk to gain 20% by selling the mixture at cost price. Then ratio of water to milk in mixture, is:

4:5

2:5

1:5

5:2

✅ Correct Option: 3

Let Cost Price of 1 liter of milk = $\text{₹}1$

Cost of water = $\text{₹}0$ (free)

Consider a mixture with:

Milk = $M$ liters

Water = $W$ liters

Actual cost = $M \times 1 + W \times 0$

Actual cost = $\text{₹}M$

The mixture is sold at cost price of milk, meaning $\text{₹}1$ per liter.

Total mixture = $(M + W)$ liters

Selling price = $(M + W) \times 1$

Selling price = $\text{₹}(M + W)$

Profit = Selling Price - Cost Price

Profit = $(M + W) - M$

Profit = $\text{₹}W$

Given that profit percentage is $20\%$ :

$\text{Profit \%} = \dfrac{\text{Profit}}{\text{Cost Price}} \times 100$

$20 = \dfrac{W}{M} \times 100$

$\dfrac{20}{100} = \dfrac{W}{M}$

$\dfrac{1}{5} = \dfrac{W}{M}$

Therefore, the ratio of water to milk is:

$W : M = 1 : 5$

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