Question

A man sells an article at 5% above its cost price. If he had bought it at 5% less than what he
paid for it and sold it at 2 less, he would have gained 10%. Find the cost price of the article.
​

Answer 1

Let the C.P. of the article be Rs. x .

Profit = 5%

$\sf{SP = \dfrac{(100 + Profit\%)}{100} \times C.P}$

$\implies \sf{SP = \frac{(100 + 5)}{100} \times x}$

$\implies \sf{SP = \dfrac{105}{100} x}$

$\implies \sf{SP = \dfrac{21}{20}x }$

If he buy article at 5% less, then

$\implies \sf{C.P = x - \dfrac{5x}{100} }$

$\implies \sf{C.P = \dfrac{100x - 5x}{100} }$

$\implies \sf{C.P = \dfrac{95}{100}x }$

$\implies \sf{C.P = \dfrac{19}{20}x }$

$\star \: \sf{New \: gain =10 \% = \dfrac{19x}{20} \times \dfrac{10}{100} = \dfrac{19x}{200} }$

$\boxed{ \sf{ \therefore \: New \: S.P = C.P + Profit }}$

$= \dfrac{19x}{20} + \dfrac{ 19x}{200}$

$= \dfrac{190x + 19x}{200}$

$= \dfrac{209}{200} x$

Now,

$\sf{Old \: S.P - New \: S.P \: \: ( Given)}$

$\rightarrow \sf{\dfrac{21}{20} x - \dfrac{209}{200} x = 2}$

$\rightarrow \sf{ \dfrac{210 - 209}{200} x = 2}$

$\rightarrow \sf{ \dfrac{x}{200} = 2 }$

$\rightarrow \sf{x = 2 \times 200}$

$\rightarrow \sf{x = 400}$

Hence, the Original C.P C.P of the article is R.s 400