Question

A book was sold for Rs.27.50 with a profit of 10%. If it were sold for Rs25.75, then what would have been the percentage of profit or loss?
(a) 4.5%
(b) 5.0%
(c) 3.0%
(d) 3.25%

Answer 1

Hint:We will first find the cost price of the book by using the formula $\text{Profit = }{\displaystyle \frac{\text{selling price - purchase price}}{\text{purchased price}}}\times 100$ after that we will compare it with Rs25.75 and try to figure the profit or loss percentage.

Complete step-by-step answer:
It is given in the question that a book was sold for Rs27.50 with a profit of $10\mathrm{\%}$. Also, if the book was sold for Rs25.75 then we have to find the percentage of profit or loss.
Basically, we will first try to find out the cost price of the book, then we will compare cost price with Rs.25.75 and if $\text{Cost Price}>Rs.25.75$ then it is a loss and we will find loss percentage, otherwise, if $\text{Cost Price}<Rs.25.75$ then it is a case of profit and we will find profit percentage.
Since, book is first sold at a profit of 10% for Rs.27.50, now let us assume that the cost price of the book be x, then we know that we can write $\text{Profit = }{\displaystyle \frac{\text{selling price - purchase price}}{\text{purchased price}}}\times 100$, that is,
$$10={\displaystyle \frac{27.5-x}{x}}\times 100$$, solving further, we get
$10x=2750-100x$, transposing 100x from RHS to LHS, we get,
$110x=2750$, that is
$x={\displaystyle \frac{2750}{110}}=25$
Thus, the cost price of the book will be Rs.25.
Now, we know that $Rs25<Rs25.75$, therefore the book is sold again with a profit of $Rs.25.75-Rs.25=Rs.0.75$ , we know that $\text{Profit}\mathrm{\%}={\displaystyle \frac{\text{profit}}{\text{CostPrice}}}\times 100$ , therefore we get % profit as
$\text{Profit}\mathrm{\%}={\displaystyle \frac{0.75}{25}}\times 100=0.03\times 100=3\mathrm{\%}$ .
Therefore, the book is sold at a profit of 3% and option c) is the correct answer.

Note: Students may assume the cost price of book as Rs.27.5 and the selling price of book as Rs.25.75 which is not correct at all. Both are different cases as clearly mentioned in the question. Thus it is recommended to read and understand the question carefully before solving it.