 QUESTION

# Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20 % and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.(a) Rs 550, Rs 750(b) Rs 550, Rs 700(c) Rs 500, Rs 750 (d) Rs 500, Rs 750

Hint: Take the cost price of one box as Rs $x$ and the cost price of another box as $1300-x$. And then applying the selling price formula because it is given in the question that the selling price of both the boxes is the same.

Before proceeding with the question, we should know the definition of cost price, selling price, profit and loss.
The price at which any article is purchased is its cost price (C.P).
The price at which any article is sold is its selling price (S.P).
Profit is the difference between S.P. and C.P., if S.P. is greater than C.P.
Loss is the difference between C.P and S.P., if C.P. is greater than S.P.
Let the C.P of first box $=x$,
Now the C.P of the second box $=1300-x$.
Now selling price (S.P) of first box $=\dfrac{100+\text{Profit}%}{100}\times \text{C}\text{.P}........(1)$
As profit is 20% in the first box, substituting this in equation (1) we get,
$\,\Rightarrow \dfrac{100+20}{100}\times x=\dfrac{120}{100}x........(2)$
And selling price(S.P) of second box $=\dfrac{100-\text{loss}%}{100}\times \text{C}\text{.P}........(3)$
As loss is 12% on the second box, substituting this in equation (3) we get,
$\,\Rightarrow \dfrac{100-12}{100}\times (1300-x)=\dfrac{88}{100}\times (1300-x)........(4)$
It is mentioned in the question that the selling price of both the boxes is the same. So now equating equation (2) and equation (4) we get,
$\,\Rightarrow \dfrac{120}{100}x=\dfrac{88}{100}\times (1300-x)........(5)$
Cancelling similar terms in equation (5) we get,
$\,\Rightarrow 120x=88\times (1300-x)........(6)$
Rearranging equation (6) and solving for x we get,
\begin{align} & \,\Rightarrow 120x+88x=88\times 1300 \\ & \,\Rightarrow 208x=114400 \\ & \,\Rightarrow x=\dfrac{114400}{208}=550 \\ \end{align}
Hence C.P of the first box is Rs 550 and C.P of another box is $1300-550=750$.
Correct option is option (a).

Note: Grasping the concept of cost price and selling price is important and knowing the relationship between profit/loss and S.P and how it relates to C.P is the key here. The question is straightforward so the only mistake we can commit is basic calculation mistakes and hence we need to do each and every step.