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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
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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, $\begin{aligned}&\%\text{ gain }=x\times\frac{100}{50}\\ &10=\frac{100\mathrm{x}}{50}\\ &\text{ Or, }2x=10\\ &\text{ or, }x=5\mathrm{~kg}\text{ . }\end{aligned}$

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