Questions & Answers

Question

Answers

Answer
Verified

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 $

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.