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A shop-keeper purchases $$11$$ knives in Rs. $$10$$ and sells them at the rate of $$10$$ knives for Rs.$$11$$. He earns a profit of

A
$$21$$ %
B
$$15$$ %
C
$$11$$ %
D
$$25$$ %
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Solution
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Correct option is A. $$21$$ %
Rate of cost price of knives = Rs 10 for 11 knives.

So, Cost Price (CP) for a knives $$=\dfrac{10}{11}\ Rs$$

Rate of selling price of knives = Rs 11 for 10 knives.

So, Selling Price (SP) for a pen $$=\dfrac{11}{10}\ Rs$$

$$\therefore Profit = SP-CP=\dfrac{11}{10}-\dfrac{10}{11}=\dfrac{121-100}{110}=\dfrac{21}{110}\ Rs$$

$$\Rightarrow Profit\ percentage = \dfrac{Profit\times 100}{CP}=\dfrac{\dfrac{21}{110}\times 100}{\dfrac{10}{11}}=21\%$$

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