Question

By selling a cycle for Rs.$2040$. I lose $15\% $of my investment. What should be my selling price if I want to make a gain of $10\% $?

Answer 1

Hint: In order to find out the selling price, at the very first we need to find the cost price of the cycle.
\[{\text{Selling price = Cost Price + Profit}}\]

Complete step-by-step answer:
Let us consider that the cost price of the cycle be Rs. $x$.
As it is stated in the question that the cycle was sold at $15\% $ loss
So we need to deduct it from the cost price which will be equal to Rs. $2040$.
Therefore we can write,
$x - \dfrac{{15}}{{100}}x = 2040$
After doing LCM we get-
$\dfrac{{100x - 15x}}{{100}} = 2040$
Now by doing cross multiplication we get-
$100x - 15x = 2040x100$
Now by doing subtraction on the left hand side we get-
$85x = 2040x100$
Therefore \[x = \dfrac{{2040x100}}{{85}}\]
On multiplying the numerator term we get,
\[x = \dfrac{{204000}}{{85}}\]
Let us divided we get,
$ = 2400$
So, the cost price of the cycle is Rs.$2400$
As per the question, to make a profit of $10\% $we have to add it with the cost price.
Also, we know selling price= Cost Price$ + $Profit
Therefore selling price= $2400 + \left( {\dfrac{{10}}{{100}} \times 2400} \right)$
On some simplifying we get,
$ = 2400 + 240$
Let us add the terms we get,
$ = 2640$

Thus we get that to make a gain of $10\% $ the cycle has to be sold at a selling price of Rs.\[2640\].

Note: It is a simple arithmetic question of profit and loss and can be easily solved by forming an equation with the help of which cost price can be easily found out and after that we can get the selling price by applying the formula, Selling price$ = $Cost price $ + $Profit.
This sum can also be solved by considering the cost price as $100$ instead of considering it as $x$.
If C.P is greater than S.P, loss is seen.
If S.P is greater than C.P, profit is seen.