Question

How many kgs of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg, gain 25% on the outlay?

Answer 1

Hint: In the above question we have a mixture of two types of salt having different prices. Here, assume the amount of salt to be mixed at $42$ paise per kg be $x$. Then calculate the cost. Apply the profit % formula as we have cost price, selling price, and profit % given. Find unknown x by solving the equation.

Complete step by step solution:
 Let the amount of salt to be mixed at $42$ paise per kg be $x$.
Given, amount of salt at $24$ paise per kg =$ 25 kg$
Total cost price of both type of salt = amount $\times$ price
$ = (x \times 42) + (25 \times 24)$
$ = 42x + 600$ …(i)
Total amount of salt after mixing = $(x + 25)$ kg
Price at which mixed salt to be sold = $40$ paise per kg
Selling price of the mixed salt = $40(x + 25)$ …(ii)
Given, Profit on mixed salt =$ 25\%$
[Profit = Selling price – Cost price]
Profit percent $ = \dfrac{{S.P - C.P}}{{C.P}} \times 100$
Putting the value of C.P and S.P from equation (i) and equation (ii), we get;
$ \Rightarrow 0.25 = \dfrac{{40(x + 25) - \left( {42x + 600} \right)}}{{42x + 600}}$
By cross multiplying, we get
$ \Rightarrow 40x + 1000 - 42x - 600 = 0.25(42x + 600) $
$ \Rightarrow 400 - 2x = 10.5x + 150 $
$ \Rightarrow 12.5x = 250$
$ \Rightarrow x = 20 $

$\therefore $ The amount of salt to be mixed at 42 paise per kg is 20 kg.

Note:
In these types of questions, where profit % and loss % are given, always remember these are calculated n cost price. Cost price is the price at which a product is purchased. It is abbreviated as C.P. Selling price is the price at which the product is sold. It is abbreviated as S.P.
Profit = S.P – C.P
Loss = C.P – S.P.