Question

a retailer purchased 25 identical toys for a price Rs P and sold some of them for Rs P. if he calculated his profit as 8%, with selling price as base instead of cost price then how many toys did he sell​

Answer 1

what is the total cost for all toys

Answer 2

SOLUTION

GIVEN

• A retailer purchased 25 identical toys for a price Rs P
• He sold some of them for Rs P.
• He calculated his profit as 8%, with selling price as base instead of cost price

TO DETERMINE

The number of toys he sold

EVALUATION

Here it is given that

A retailer purchased 25 identical toys for a price Rs P

So the cost price of each toys

$= \displaystyle \sf{Rs \: \: \frac{P}{25} \: \: }$

Suppose he sold n toys for Rs P

So the selling price of each of the n toys

$= \displaystyle \sf{Rs \: \: \frac{P}{n} \: \: }$

Now He calculated his profit as 8%, with selling price as base instead of cost price

So the profit

$= \displaystyle \sf{Rs \: \bigg( \frac{P}{n} \times \frac{8}{100} \bigg)\: }$

So by the given condition

$\displaystyle \sf{\frac{P}{n} \: } - \frac{P}{25} = \bigg( \frac{P}{n} \times \frac{8}{100} \bigg)$

$\implies\displaystyle \sf{\frac{P}{n} \: } - \bigg( \frac{P}{n} \times \frac{8}{100} \bigg) = \frac{P}{25}$

$\implies\displaystyle \sf{\frac{P}{n} \: } \bigg( 1 - \frac{8}{100} \bigg) = \frac{P}{25}$

$\implies\displaystyle \sf{\frac{P}{n} \: } \times \bigg( \frac{92}{100} \bigg) = \frac{P}{25}$

$\implies\displaystyle \sf{\frac{1}{n} \: } \times \bigg( \frac{92}{100} \bigg) = \frac{1}{25}$

$\implies\displaystyle \sf{n = 25 \times \bigg( \frac{92}{100} \bigg) }$

$\implies\displaystyle \sf{n = 23 }$

FINAL ANSWER

The number of toys the retailer sold for Rs P is 23

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