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1. A shopkeeper sold an item for Rs. 1510 after giving a discount of $24 \frac{1}{2} %$ and there by incurred a loss of 10%. Had he sold the item without discount his net profit would have been = ?

A. Rs. 641

B. $Rs . 322 \frac{1}{9}$

C. $Rs . 422 \frac{2}{9}$

D. $Rs . 322 \frac{2}{9}$

Solution:

Let the marked price of an item = Rs. x
Selling price of an item

= (100 - 24 \frac{1}{2}) % of x

\begin{aligned} \Rightarrow 1510 = \frac{151}{2} \times \frac{1}{100} \times x \\ \Rightarrow x = Rs . 2000 \\ Cost price of an item \\ = 1510 \times \frac{100}{90} \\ =  Rs . \frac{15100}{9} \\ Without discount, gain \\ = 2000 - \frac{15100}{9} \\ = \frac{18000 - 15100}{9} \\ = \frac{2900}{9} \\ = Rs . 322 \frac{2}{9} \end{aligned}

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