## Alligation or Mixture

#### Alligation or Mixture

1. The average daily wages of staff, consisting of supervisors and labourers, of a company is Rs. 50. The average wages of supervisors is Rs. 150 while that of labourers is Rs. 40 per day. If the number of supervisors is 15, find the number of labourers in the company.

1. As per figure we can calculate the ration as below.
Number of supervisors / Number of labourers = (10 / 100) = 1/10

##### Correct Option: A

As per figure we can calculate the ration as below.
Number of supervisors / Number of labourers = (10 / 100) = 1/10
Total number of labourers = Total no. of supervisors × 10
= 15 × 10 = 150.

1. 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. Average rate of interest = (100 * 750) / (5000 * 3) = 5% per annual

##### Correct Option: C

Average rate of interest = (100 * 750) / (5000 * 3) = 5% per annual
Investment at 3% per annual = 3 / (3 + 2) × 5000 = Rs. 3000 Investment at 8% per annual = 2 / (3 + 2) × 5000 = Rs. 2000

1. A man bought a certain quantity of sugar for Rs. 8000. He sells one-fourth of it at 20% loss. At what per cent profit should he sell the remainder stock so as to make an overall profit of 20%?

1. Let the remainder stock be sold at P% profit.
(P - 20) / 30 = ((1 / 4) / (3 / 4))

##### Correct Option: B

Let the remainder stock be sold at P% profit.
(P - 20) / 30 = ((1 / 4) / (3 / 4))
or (P – 20) = 30 × (1 / 3)
or P = 20 + 10
P = 30% profit.

1. A merchant has 160 kgs of wheat. He sells a part of it at 10% profit and the rest of 6% loss. If he incurs 4% loss on the whole, find the quantity for each part.

1. According to figure we can find that the ration would be 1 : 7.

##### Correct Option: B

According to figure we can find that the ration would be 1 : 7.
Quantity sold at 10% profit = 1 / (1 + 7)× 160 = 20 kgs.
Quantity sold at 6% loss = (160 – 20) = 140 kgs.

1. A person has two solutions of sugar with 30% and 50% concentration respectively. In what proportion should he mix two solutions to get 45% concentration in the resulting mixture?

1. He should mix 30% and 50% in the ratio 5 : 15

##### Correct Option: A

He should mix 30% and 50% in the ratio 5 : 15 or 1 : 3.
( 30% Solution ) / (50% Solution) = 1 / 3 or 1 : 3