Question

A scooty is sold for 13,600 and fetches a loss of $ 15\% $ . Find the cost price of the scooty.

Answer 1

Hint: Loss occurs when the selling price is less than the cost price. And the lost percentage is the ratio of the difference between the selling price and cost price to the cost price. Assume cost price to be some variable. Then find the loss amount in terms of that variable. Then compare the ratio of loss and cost price with the loss percentage to find the value of the variable taken.

Complete step-by-step answer:
Let the cost price of the scooty be $ x $
We know that
 $ loss\% = \dfrac{{CP - SP}}{{CP}} $
Where,
 $ CP $ is cost price
 $ SP $ is sells price
It is given in the question that,
The scooty is sold at the selling price, $ SP = 13600 $
 At the loss of $ 15\% $
By substituting the value of in the above equation, we get
 $ 15\% = \dfrac{{x - 13600}}{x} $
 $ \Rightarrow \dfrac{{15}}{{100}} = \dfrac{{x - 13600}}{x} $
By cross multiplying, we get
 $ 15x = 100x - 1360000 $
On simplifying it, we get
 $ 85x = 1360000 $
By dividing both the sides by 85 we get
 $ x = 16000 $
Therefore, the cost price of the scooty was ₹ 16000

Note: The formula of profit percentage and loss percentage is the same. In such a case, when you calculate the loss percentage the answer comes negative. It doesn’t mean that the answer is wrong. The negative sign in such a case represents loss and the positive sign represents profit. To avoid this confusion, you can subtract the selling price from the cost price and get a positive answer. Both the ways are correct. But don’t forget to write the profit or loss in percentage and then convert is into a fraction by dividing by 100. In the above question if you just write 15 in loss. Then the answer would be incorrect.