Question

After incurring a loss of \[25\% \], a man had rupees \[Rs.18000\] left with him. What was the amount of money he originally had?

Answer 1

Hint: The loss for any product is given when selling price is less than cost price as \[loss = c.p - s.p\] and the loss in percentage is given as \[loss = \dfrac{{c.p - s.p}}{{c.p}} \times 100\]. As the final amount left is given as \[Rs.18000\]. And the percentage loss is given. By using the loss percentage formula we will get the required solution.

Complete step by step answer:

As given that a man had rupees \[Rs.18000\]left with him and he is incurring a loss of \[25\% \]
Hence, using loss percentage formula \[loss = \dfrac{{c.p - s.p}}{{c.p}} \times 100\] as,
Let the cost price be x.
The S.P is \[Rs.18000\] , and the loss percentage is \[25\% \],
So substituting the values in \[loss = \dfrac{{c.p - s.p}}{{c.p}} \times 100\], we get,
\[ \Rightarrow \]\[25 = \dfrac{{x - 18000}}{x} \times 100\]
On dividing the equation by 100 we get,
\[ \Rightarrow \]\[\dfrac{1}{4} = \dfrac{{x - 18000}}{x}\]
Hence, on further simplification, we get,
\[ \Rightarrow \]\[\dfrac{1}{4} = 1 - \dfrac{{18000}}{x}\]
Hence, on rearranging we get,
\[ \Rightarrow \]\[\dfrac{3}{4} = \dfrac{{18000}}{x}\]
On cross multiplying, we get,
\[ \Rightarrow \]\[3x = 72000\]
\[ \Rightarrow \]\[x = \dfrac{{72000}}{3}\]
Hence, on dividing, we get,
\[ \Rightarrow \]\[x = c.p = Rs.24000\]
Hence, \[Rs.24000\] is the amount man originally had in the very starting.

Note: Cost Price: The price at which an article is purchased, is called its cost price (C.P.).
Selling Price: Price at which an article is purchased is known as its selling price (S.P.).
The extra money earned by selling an article is called profit or gain. When Selling Price (S.P.) is greater than the Cost Price (C.P.) .