CAT 2016 | Question: 70

Question

Instead of a metre scale, a cloth merchant uses a $120\; \text{cm}$ scale while buying, but uses an $80\; \text{cm}$ scale while selling the same cloth. If he offers a discount of $20 \%$ on cash payment, what is his overall profit percentage?

• A. $20\%$
• B. $25\%$
• C. $40\%$
• D. $15\%$

Answer 1

Let the cost price of $1$ meter ($100$ cm) cloth be ₹ $100$.

So, the cost price of $120$ cm cloth is ₹ $100$.

The selling price of $80$ cm cloth $=80\%$ of ₹ $100=\dfrac{80}{100}\times100=$ ₹ $80$.

Cost price of $80$ cm cloth $= \dfrac{100}{120}\times80 = $₹ $\frac{200}{3}$

$\therefore$ Profit percentage $= \left(\dfrac{\text{SP – CP}}{\text{CP}}\right)\times100\%$

$\qquad \qquad \qquad \quad = \left(\dfrac{80-\frac{200}{3}}{\frac{200}{3}}\right)\times100\%$

$\qquad \qquad \qquad \quad = \left(\dfrac{\frac{240-200}{3}}{\frac{200}{3}}\right)\times100\%$

$\qquad \qquad \qquad \quad = \require{cancel} \dfrac{\cancel{40}^{20}}{\cancel{3}}\times\dfrac{\cancel{3}}{\cancel{2}\cancel{00}}\times1\cancel{00}\%$

$\qquad \qquad \qquad \quad=20\%.$

Correct Answer: $\text{A}$