### Mixtures questions and its solutions

Formulae and shortcuts used to solve the following problems are discussed in the previous post.

**Solved Problems**

1. Let the cost of 2 quantities of rice be Rs.15 and Rs.19 per kg. Find the ratio of mixture which cost Rs.18 per kg?

Soln.:

__Method1:__

Let the quantity of rice of quality A (Rs.15/kg) be 'x'

Let the quantity of rice of quality B (Rs.19/kg) be 'y'

As per the problem, 15x+19y = 18(x+y)

y = 3x => x/y = 1/3

Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.

__Method2:__Using shortcut,

Therefore, ratio is 1:3

2. Let the cost of 2 quantities of rice be Rs.15 (quality A) and Rs.19 (quality B) per kg. Find the quantity of rice of quality A that has to be mixed with 27kg of quality B to make the cost of rice as Rs.18?

Soln.:

__Method1:__

Let the quantity of rice of quality A (Rs.15/kg) be 'x'

Let the quantity of rice of quality B (Rs.19/kg) be 'y'

As per the problem, 15x+19y = 18(x+y)

y = 3x => x/y = 1/3

Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.

=> 3 parts of quality B is to be mixed with 1 part of quality A

=> 27kg of quality B is to be mixed with 9kg of quality A.

Ans: 9kgs

__Method2:__Using shortcut,

Therefore, ratio is 1:3

=> 3 parts of quality B is to be mixed with 1 part of quality A

=> 27kg of quality B is to be mixed with 9kg of quality A.

Ans: 9kgs

3. Let the cost of 2 quantities of rice be Rs.15 and Rs.19 per kg. These 2 qualities of rice are mixed and sold at Rs.27 per kg of profit 50%. Find the ratio in which 2 qualities of rice mixed?

Soln.:

__Method1:__

Let the quantity of rice of quality A (Rs.15/kg) be 'x'

Let the quantity of rice of quality B (Rs.19/kg) be 'y'

Given Selling price, SP = 27 and the profit % is 50%

We know that the profit%, p% = (SP-CP)/CP * 100

=> 50/100 = (27 - CP)/CP

=> CP = 18

As per the problem, 15x+19y = 18(x+y)

y = 3x => x/y = 1/3

Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.

__Method2:__Using shortcut,

Given Selling price, SP = 27 and the profit % is 50%

We know that the profit%, p% = (SP-CP)/CP * 100

=> 50/100 = (27 - CP)/CP

=> CP = 18

Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.

4. A man purchased TV and Washing machine for Rs.30000. He sold the TV at 30% profit and washing machine at 60% profit. He makes overall profit of 50%. Then find for how much did he purchased TV and washing machine?

Soln:

__Method1:__

Let the cost price of TV be 'x'

Let the cost price of washing machine be 'y'

As per the problem,

x + y = 30000 ------> Eq. 1

SP of TV = 1.3x

SP of washing machine = 1.6y

1.3x + 1.6y = 30000 * 1.5

1.3x + 1.6y = 45000 --------> Eq. 2

On solving equations 1 and 2, x = 10000 and y = 20000

Therefore, cost price of TV and washing machine are Rs.10000 and Rs.20000 respectively.

__Method2:__Using shortcut,

Therefore, ratio is 1:2. 3 parts is equivalent to 30000

=> Cost of TV is 10000 (1 part) and Cost of washing machine is 20000 (2 parts)

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