Question

Mahesh sells a quintal of rice for 924 and earns a profit of 12%. By selling a quintal of wheat for the same amount, he lost 12%. Find
A. CP of 1 kg of rice
B. CP of 1 kg of wheat
C. Mahesh's overall profit or loss percent

Answer 1

Hint: In such questions we use the concept of profit and loss.
In part (a), first, find the cost price by the formula, $\dfrac{{100}}{{100 + P\% }} \times SP$, then divide the cost price by 100 to get the cost price of 1 kg of rice.
In part (b), first, find the cost price by the formula, $\dfrac{{100}}{{100 + L\% }} \times SP$, then divide the cost price by 100 to get the cost price of 1 kg of wheat.
In part (c), find the total cost price and selling price of both rice and wheat by adding them. Then, compare them to find whether there is a gain or loss. After that find the profit or loss percent according to it.

Complete step-by-step solution:
Given: - Mahesh sells a quintal of rice and wheat for Rs 924.
He earns a profit of 12% on rice and a loss of 12% on wheat.
(A) The formula to calculate the cost price is,
$CP = \dfrac{{100}}{{100 + P\% }} \times SP$
Substitute the values,
$ \Rightarrow CP = \dfrac{{100}}{{100 + 12}} \times 924$
Add the terms in the numerator,
$ \Rightarrow CP = \dfrac{{100}}{{112}} \times 924$
Simplify the terms,
$\therefore CP = 825$
So, the cost price of a quintal of rice is Rs. 825.
Now, the cost of 1 kg of rice is,
$ \Rightarrow $ Cost of 1 kg of rice $ = \dfrac{{825}}{{100}}$
Divide the numerator by denominator,
$ \Rightarrow $ Cost of 1 kg of rice $ = 8.25$
Hence, the cost price of 1 kg of rice is Rs. 8.25.
(B) The formula to calculate the cost price is,
$CP = \dfrac{{100}}{{100 - L\% }} \times SP$
Substitute the values,
$ \Rightarrow CP = \dfrac{{100}}{{100 - 12}} \times 924$
Add the terms in the numerator,
$ \Rightarrow CP = \dfrac{{100}}{{88}} \times 924$
Simplify the terms,
$\therefore CP = 1050$
So, the cost price of a quintal of wheat is Rs. 1050.
Now, the cost of 1 kg of wheat is,
$ \Rightarrow $ Cost of 1 kg of wheat $ = \dfrac{{1050}}{{100}}$
Divide the numerator by denominator,
$ \Rightarrow $ Cost of 1 kg of wheat $ = 10.50$
Hence, the cost price of 1 kg of wheat is Rs. 10.50.
(C) The total selling price will be the sum of the selling price of rice and wheat,
$ \Rightarrow $ Total selling price $ = 924 + 924$
Add the terms,
$ \Rightarrow $ Total selling price $ = 1848$
The total cost price will be the sum of the cost price of rice and wheat,
$ \Rightarrow $ Total cost price $ = 825 + 1050$
Add the terms,
$ \Rightarrow $ Total cost price $ = 1875$
Since, Total Cost Price > Total Selling Price. Then,
$ \Rightarrow $ Loss $ = TCP - TSP$
Substitute the value,
$ \Rightarrow $ Loss $ = 1875 - 1848$
Subtract the values,
$ \Rightarrow $ Loss $ = 27$
The loss percentage can be calculated by the formula,
$Loss\% = \dfrac{{loss}}{{TCP}} \times 100$
Substitute the values,
$ \Rightarrow Loss\% = \dfrac{{27}}{{1875}} \times 100$
Simplify the terms,
$ \Rightarrow Loss\% = 1.44\% $
Hence, Mahesh’s overall loss percent is 1.44%.

Note: Cost Price: The price at which an article is purchased, is called its cost price (C.P.).
Selling Price: The price at which an article is purchased is known as its selling price (S.P.).
Profit or Gain: If SP is greater than CP then the seller is said to have profit or gain.
\[Profit = SP - CP\]
\[Profit\% = \dfrac{{Profit}}{{CP}} \times 100\]