### 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

### 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

A. 2 : 5
B. 3 : 5
C. 5 : 3
D. 5 : 2

### 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:

A. $\large\frac{1}{2} \mathrm{~kg}$
B. $\large\frac{1}{8} \mathrm{~kg}$
C. $\large\frac{3}{14} \mathrm{~kg}$
D. $\large\frac{7}{9} \mathrm{~kg}$

A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres