Question

A shopkeeper offers his customers $10\%$ discount and still makes a profit of $26\%$. What is the actual cost of an article marked Rs. 280? [4 MARKS]

Answer 1

Formula : 1 Mark
​Application : 1 Mark
Calculation : 2 Marks

We have,

Marked price = Rs. 280, Discount $=10\%$

$\therefore S.P.=MP\times \left(\frac{100-Discount\%}{100}\right)$

$\Rightarrow S.P.=Rs\{280\times \left(\frac{100-10}{100}\right)\}=Rs\left\{\frac{280\times 90}{100}\right\}=Rs252$

Now, S.P. = Rs. 252 and Gain $=26\%$

$\therefore C.P.=\frac{100}{100+Gain\%}\times S.P.$

$\Rightarrow C.P=Rs(\frac{100}{100+26}\times 252)=Rs(\frac{100}{26}\times 252)=Rs.200$

Hence, the actual cost of the article is Rs. 200