In this post we will to solve profit and loss questions using Mixtures and Alligation concept. Using the concept will help us to solve question fast which will help save time in the examination hall.

All the questions are solved step by step for your understanding. But in case if you feel lost, i will suggest you to read theory about this chapter given in sub page.

## Mixture and Alligations Questions

**(01) In what proportion water be mixed with milk to gain 12.5 % by selling it at cost price?**

Given:

Profit = 12.5%

Let the cost price of milk = Re. 1

Let the selling price of mixture = Re. 1

Gain = 12.5%

So, Cost price of mixture would be = [100/ (100 + 12.5)] x 1

= (100/ 112.5) x 1

= 8/ 9

Using Mixture and allegations

Therefore ratio = n_{1}/ n_{2}

= (8/9)/ (1/9)

Milk: water = 8: 1

Or water: Milk = 1: 8

**Ans. Hence, the ratio of water and milk would be 1:8**

**(02) Mr. Yadav purchased two book factories, one in India and other one in China for total Rs. 72 crores. Later on, he sold the Indian factory at 16% profit and Chinese factory at 24% profit. Thus, he gained a total profit of 19%. The selling price of Indian factory is**?

Given:

CP of two book factories = Rs. 72 crores

Overall profit = 19 %

Ratio of Cost Prices = 5: 3

Cost price of Indian factory = [72/ (5 + 3)] x 5 [(CP/ Sum of ratios) x n_{1}]

= 45 crores

Selling Price = 45 x [(100 + 16)/ 100]

= (45 x 116)/ 100

= 52.20 crore

**Ans. The selling price of Indian factory is Rs. 52.20 crores.**

**(03) The price of petrol is Rs. 60 per litre and the price of oil is Rs. 40 per litres. In what ratio the petrol and oil be mixed such that the profit after selling the mixture at Rs. 75 per litre be 25%?**

**Sol.** Given: Selling Price of mixture = Rs. 75 per litre

Profit = 25% or I.e., if CP is Rs.4 than profit must be Rs.1 I.e., 1/ 4

CP = 75 x (4/ (4 + 1)) [SP x (CP/ (CP + Profit))]

= 75 x (4/ 5)

= Rs. 60

By allegations,

Now we know that if we mix oil (worth Rs. 40 per litres) with petrol (worth Rs. 60 per litres), the cost price of the mixture must be less than Rs. 60 per litres, which is impossible.

**Ans. Hence required condition is impossible.**

**(Qu.4) A trader sells total 315 TV sets. He sells black and white TV sets at a loss of 6% and color TV sets at a profit of 15%. Thus, he gains 9% on the whole. The no. of black and white TV sets, which he has sold is :**

Total TV sold by trader = 315

Ratio of quantities = 6: 15

= 2: 5

Now, Total TVs sold = 315

(2 + 5) units = 315

7 units = 315

1 unit = 315/ 7

= 45

Therefore, total no. Of black and white TV set sold = 45 x 2 = 90

**Ans. Total 90 sets of black and white TVs sold.**

**Qu.5) How many kilograms of sugar worth Rs. 3.60 per kg should be mixed with 8 kg of sugar worth Rs. 4.20 per kg. such that by selling the mixture at Rs. 4.40 per kg, there may be a gain of 10%?**

Selling Price of mixture = Rs. 4.40 per kg

Profit = 10 %

Cost Price of mixture of 1 kg = [100/ (100 + Profit%)] x SP

= [100/(100 + 10)] x 4.40

= Rs.4

Ratio of cost prices = n1/ n2 = 0.2/ 0.4

= 1: 2

Therefore, sugar to be mixed = Ratio of its CP x CP of mixture of 1 kg

= 1 x 4

= 4 kg

**Ans. Required quantity of sugar to be mixed is 4 kg.**