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: Here first we will assume the cost price to be x Rs. Then we will use the concept of loss and profit to make the equations and then solve for x. Then finally we will find the selling price by substituting the value of x.
\[{\text{Profit}} = {\text{selling price}} - {\text{cost price}}\]
\[{\text{loss}} = {\text{cost price}} - {\text{selling price}}\]

Complete step-by-step answer:
Let the cost price of the cycle be x.
Now it is given that there is a 15% loss on selling the cycle for Rs. 2040
Hence here, the selling price is Rs. 2040 and the cost price is x and the loss is \[\dfrac{{15}}{{100}}x\]
Now we know that:-
\[{\text{loss}} = {\text{cost price}} - {\text{selling price}}\]
Hence putting in the respective values we get:-
\[\dfrac{{15}}{{100}}x = x - 2040\]
Solving for x we get:-
\[2040 = x - \dfrac{{15}}{{100}}x\]
\[ \Rightarrow 2040 = x - \dfrac{3}{{20}}x\]
Taking LCM we get:-
\[\dfrac{{20x - 3x}}{{20}} = 2040\]
Simplifying it further we get:-
\[17x = 2040 \times 20\]
\[x = \dfrac{{2040 \times 20}}{{17}}\]
\[x = 2400\]
Therefore, the cost price of the cycle is Rs. 2400
Now it is given that we have to make a gain of 10%.
Therefore, the gain can be calculated by:-
\[gain = 10\% {\text{ of 2400}}\]
This implies, \[gain = \dfrac{{10}}{{100}} \times 2400\]
Solving it we get:-
\[gain = Rs. 240\].
Now we know that,
\[{\text{Profit}} = {\text{selling price}} - {\text{cost price}}\]
Hence putting the respective values we get:-
\[240 = {\text{selling price}} - 2400\]
Solving for selling price we get:-
\[{\text{selling price}} = 2400 + 240\]
\[{\text{selling price}} = Rs. 2640\].
Hence the selling price should be Rs. 2640

Note: Students should note that selling price has to be greater than the cost price order to gain profit and the cost price should be greater than the selling price in case of loss.