Question

By selling a watch for \[Rs.1440\], a man loses \[10\%\]. At what price should he sell, to gain \[5\%\]?

Answer 1

Hint: We are given that man faces a loss of \[10\%\] when he sells a watch, which means that he has sold his watch less than the cost price. In order to earn a profit, he has to sell it at a price more than his cost price. So let us find each of the prices and obtain a price at which he gains \[5\%\].

Complete step-by-step solution:
Let us see what the terms actually mean that are mentioned in our given question.
Cost Price: The price at which goods are or have been bought by a merchant or retailer is known as cost price.
Selling Price: It is the price at which a good or commodity is sold by a shopkeeper to a customer.
Loss occurs when the goods are sold at less than cost price and profit occurs when the selling price is more than the cost price.
Now, let us find the selling price at which the man can earn a profit of \[5\%\].
From the question, we have
Selling price of watch at \[10\%\] loss =\[1440\]
loss \[\%\]=\[10\%\]
the cost price of watch is-
SP= \[100-10=90\%\]
SP = \[1440\](GIVEN)
\[\begin{align}
  & 90\%=1440 \\
 & 1\%\text{ }=\text{ }1440\text{ }\div ~90\text{ }~=\text{ }16 \\
 & 100\%\text{ }=\text{ }16\text{ }\times \text{ }100 \\
\end{align}\]
\[\therefore \] We get the cost price = \[1600\]
So, we can say that the new selling price is calculated as
Profit = \[5\%\]
Profit= \[5\%\text{ }of\text{ }Rs\text{ }1600\text{ }=\text{ }5\text{ }\times \text{ }16\text{ }=~\mathbf{Rs}.~\mathbf{80}\]
Selling price = Cost price + Profit
Selling price =
\[\begin{align}
  & 1600+80 \\
 & =1680 \\
\end{align}\]
\[\therefore \] The man should sell the watch at \[\mathbf{Rs}.~1680\] in order to gain \[5\%\].

Note: The formulas to calculate the profit and loss percent when the selling price and cost price are given.
Profit Percent= \[~\dfrac{S.P-C.P}{C.P}\times 100\]
Loss percent= \[\dfrac{C.P-S.P}{C.P}\times 100\]