Application of Alligation

Application in profit & loss questions

Question: How many must kgs of rice costing Rs 8 per kg be mixed with 36 kg of rice costing Rs 5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs 7.20 per kg?

1. 10 kg
2. 12 kg
3. 10.8 kg
4. 8 kg

Solution:

Always remember that we need to take only the cost price and not the selling price when we consider the price of all entities in the question.In the question, the selling price of the mixture is given. We need to find out the cost price using the profit percentage given=20%. Cost price × 1.2=7.2 , implies that cost price of the mixture is 6.

From the Alligation chart,

X = 6 - 5.40 = 0.6 Y = 8 - 6 = 2

Thus the ratio between the quantity of type A rice and type B rice is 0.6:2 or 3:10 Therefore => x=10.8 kg.

Application in mixtures of liquids

Question: Vessel A contains milk and water in the ratio 4:5. Vessel B contains milk and water in the proportion 5:1.In what proportion should quantities be taken from A & B to form a mixture in which milk and water are in the ratio 5:4?

1. 2:5
2. 3:2>/li>
3. 2:3
4. 5:2

Solution

For this question, let’s consider the proportion of milk in each mixture. In Vessel A, the proportion of milk in 4/((4+5) )=4/9.in vessel B, the proportion of milk is 5/(5+1) = 5/6.

The amount of milk in the mixture= 5/((5+4)) = 5/9

X = (5/6) - (5/9) = 5/18

Y = (5/9) - (4/9) = 1/9

The ratio is (5/18):(1/9) = 5:2

Application in percentage questions

Question: A person has Rs.5000. He invests a part of it at 3% per annum and the remainder at 8% per annum simple interest. His total income in 3 years is Rs.750. Find the sum invested at different rates of interest?

1. 3500, 1500
2. 1000, 4000
3. 3000, 2000
4. 1800, 3200

Solution

He is investing part of it at 3% at annum and remaining at 8% per annum Since he is getting Rs 750 as profit for 3 years, rate percent of the whole amount is 5%.

That can be calculated from PNR/100 = 750 ((5000 ×3 ×R))/100 = 750 R= 5%

From the Alligation chart,

The ratio of investment will be 3:2. Look at the answer options for that ratio.

The only option (C) (3000, 2000) gives that ratio.