Question

Mohan bought a certain number of notebooks for $Rs.600$. He sold $\frac{1}{4}$ 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

Answer: (B)

Rs. $517.5$

Let total number of books $=x$

Total Cost Price $=Rs.600$

Cost of each book $=Rs.\frac{600}{x}$

He sells $\frac{1}{4}$th of the books i.e. $0.25x$ at $5$% loss.

Percent loss $=\frac{Loss}{C.P}\times 100$

$\Rightarrow -\frac{5}{100}=\frac{(S.P-C.P)}{C.P}=\frac{S.P}{C.P}-1\Rightarrow \frac{S.P}{C.P}=\frac{95}{100}\Rightarrow S.P=\frac{95}{100}\times (0.25\times \left(\frac{600}{x}\right))=142.5$

He sells the remaining $0.75x$ books at some profit $p$

$S.P^{\prime }=C.P^{\prime }+\left(\frac{p}{100}\right)\times C.P^{\prime }=\left(\frac{(p+100)}{100}\right)\times (\left(\frac{600}{x}\right)\times 0.75x)S.P^{\prime }=4.5(p+100)$

Total $S.P=$ Total $C.P+10$% of $C.P$

$\Rightarrow 142.5+4.5(p+100)=600+60=660$

$\Rightarrow p+100=115$

$\Rightarrow p=15\%$

$\therefore S.P^{\prime }=4.5\left(115\right)=517.5$

So, he should sell the remaining books for $Rs.517.5$