Question

Mohan bought a certain number of notebooks for Rs. 600. He sold $\dfrac{1}{4}$ of them at 5% loss. At what price should he sell the remaining notebooks so as to gain 10% on the whole.
(a) Rs. 510
(b) Rs. 517.5
(c) Rs. 521.5
(d) Rs. 540

Answer 1

Hint: We start solving the problem by finding the price of the $\dfrac{1}{4}$th of the books which Mohan sold at a loss of 5% loss using the property that a% of b is $\dfrac{a}{100}\times b$. We then find the price that all books have to be sold in order to get the 10% gain on all of them. We then subtract the selling price of $\dfrac{1}{4}$th of the books from the selling price of total books to get the selling price of remaining books.

Complete step-by-step answer:
According to the problem, we are given that Mohan bought a certain number of notebooks for Rs. 600 and sold $\dfrac{1}{4}$ of them at 5% loss. We need to find the price to sell the remaining notebooks in order to gain 10% on the whole.
Let us find the price of $\dfrac{1}{4}$th of the books i.e., $\dfrac{1}{4}\times 600=Rs.150$.
But Mohan sold these books at 5% loss. This means that Mohan sold them at $\left( 100-5 \right)\%=95\%$ of the price he bought.
So, the price of these $\dfrac{1}{4}$th of books is 95% of Rs.150.
We know that a% of b is defined as $\dfrac{a}{100}\times b$.
So, $95\%\text{ }of\text{ }Rs.150=\dfrac{95}{100}\times 150$.
$\Rightarrow 95\%\text{ }of\text{ }Rs.150=0.95\times 150$.
$\Rightarrow 95\%\text{ }of\text{ }Rs.150=Rs.142.5$.
So, he sold $\dfrac{1}{4}$th of books for Rs. 142.5 ---(1).
Now, let us find the amount that he needs to sell all the books in order to get 10% gain.
So, the selling price of the total is $\left( 100+10 \right)\%=110\%$ of the total price of Rs. 600.
So, we get $110\%\text{ }of\text{ }Rs.600=\dfrac{110}{100}\times 600$.
$\Rightarrow 110\%\text{ }of\text{ }Rs.600=1.1\times 600$.
$\Rightarrow 110\%\text{ }of\text{ }Rs.600=Rs.660$ ---(2).
Now, let us subtract the amount that we got in equation (1) from equation (2) which will be the selling price of the remaining books.
So, the selling price of the remaining books is $Rs.\left( 660-142.5 \right)=Rs.517.5$.
We have found the selling price of remaining books as Rs. 517.5.
The correct option for the given problem is (b).

So, the correct answer is “Option (b)”.

Note: Here we had assumed that all notebooks are familiar with the same cost otherwise, the answer would be different. We should confuse a% of b as $a\times b$, which is the most common mistake done by many students. We can also find the profit occurred on the remaining $\dfrac{3}{4}$th of the books using the selling price we just obtained. Similarly, we can expect problems to find the cost price of the notebooks if Mohan got 15% profit on selling them for Rs. 700.