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Two solutions A and B are mixed in the ratio 2 : 3 by volume in litre. The C.P. of solution A is Rs. 350 per litre and that of B is Rs. 400 per litre. If one-fifth of solution is sold at Rs. 460 per litre and remaining of it at Rs. 550 per litre, find the profit percent on the whole.

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30 %

50 %

20 %

40 %

answer is C.

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Detailed Solution

Given that, two solutions

A

and

B

are mixed in the ratio

2 : 3

by volume in litre.
The

C . P .

of solution

A

Rs . 350

per litre and that of

B

Rs . 400

per litre.
One-fifth of the mixed solution is sold at

Rs . 460

per litre and remaining at

Rs . 550

per litre.
We have to find the profit percentage on the whole mixture.
Let the quantity of solution

A

2 x

litres.
Hence, the quantity of solution

B

will be

3 x

litres.
The cost of one litre of solution

A = Rs . 350

.
Hence, the cost of

2 x

litres of

A = 2 x \times 350

Rs . 700 x

.
Also, the cost of one litre of solution

B = Rs . 400

Hence, the cost of

3 x

litres of

B = 3 x \times 400

Rs . 1200 x .

Now, the total solution will be (

2 x + 3 x) = 5 x

litres.
And, the cost of

5 x

litres of the solution

= Rs . 700 x + 1200 x =

Rs . 1900 x

One-fifth of the solution is

x

litres and the remaining is

4 x

litres.
Now, one-fifth of the solution is sold at

Rs . 460

per litre.
Hence, selling price of

x

litres of solution

= x \times 460

= Rs . 460 x

Also, the remaining solution is sold at

Rs . 550

per litre.
Hence, the selling price of

4 x

litres of solution

= 4 x \times 550

Rs . 2200 x

So, the selling price of the total

5 x

litres of solution

= Rs . 460 x + 2200 x = Rs . 2660 x

So, for complete

5 x

litres of solution, we have:

C . P . = Rs . 1900 x

S . P . = Rs . 2660 x

We know that,

profit % = \frac{S . P . - C . P .}{C . P .} \times 100

\Rightarrow profit % = \frac{2660 x - 1900 x}{1900 x} \times 100

\Rightarrow profit % = \frac{760 x}{1900 x} \times 100

\Rightarrow profit % = \frac{760}{19}

\Rightarrow profit % = 40

%
Hence, the profit percent on the whole is

40 %

.
Therefore, the correct option is 3.

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Two solutions A and B are mixed in the ratio 2 : 3 by volume in litre. The C.P. of solution A is Rs. 350 per litre and that of B is Rs. 400 per litre. If one-fifth of solution is sold at Rs. 460 per litre and remaining of it at Rs. 550 per litre, find the profit percent on the whole.

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