###
**To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:**

A. 2.5 kg
B. 5 kg
C. 7.5 kg
D. 10 kg
**Answer: Option B**

## Show Answer

Solution(By Apex Team)

**1st Method (Method of Alligation):**Let the quantity of water to be mixed is x kg. Let cost of milk be Rs. 1 per kg. Then SP of 50 kg of milk with gain 10% = Rs. 55 [As Cost of 50 kg milk = Rs. 50, then SP = (50 + 10% of 50)] Then, water to be mixed is 5 kg, As the selling price of the milk is Rs. 1 per kg. Seller has to have 10% gain on 50 kg milk, he must have to add 5 kg water to 50 kg milk.

**Alternate:**

**2nd Method (Simple Method):**Let the quantity of water mixed be x kg. Let CP of 1 kg of pure milk = Rs. 1. Hence, $\begin{aligned}&\%\text{ gain }=x\times\frac{100}{50}\\ &10=\frac{100\mathrm{x}}{50}\\ &\text{ Or, }2x=10\\ &\text{ or, }x=5\mathrm{~kg}\text{ . }\end{aligned}$

## Related Questions On Alligation

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### An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:

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