Question

A man sells an article at a gain of 15%. Had he bought it at 10% loss and sold it for Rs 4 less,he would have gained 25%.the cost price of the article is

Answer 1

Given :

A man sells an article at a gain of 15%

Had he bought it at 10% loss and sold it for Rs 4 less

And

The last gain% = 25%

To Find :

The cost price of article

Solution :

Let The cost price of article = c.p

Let The selling price of article = s.p

According to question

For 15 % of gain

i.e gain% = $\dfrac{s.p-c.p}{c.p}$

Or, 15% = $\dfrac{s.p-c.p}{c.p}$

or,   $\dfrac{15}{100}$ = $\dfrac{s.p-c.p}{c.p}$

∴   $\dfrac{s.p}{c.p}$  = 1 + $\dfrac{15}{100}$

i.e  $\dfrac{s.p}{c.p}$ = $\dfrac{115}{100}$                 ............1

Similarly

For 10 % of loss

i.e loss% = $\dfrac{c.p-s.p}{c.p}$

Or, 10% = $\dfrac{c.p-(s.p-4)}{c.p}$

or,   $\dfrac{10}{100}$ = $\dfrac{c.p-(s.p-4)}{c.p}$

∴   $\dfrac{(s.p-4)}{c.p}$  = 1 - $\dfrac{10}{100}$

i.e   $\dfrac{(s.p-4)}{c.p}$= $\dfrac{90}{100}$              ...........2

From, eq 1 and eq 2

$\dfrac{(s.p-4)}{s.p}$= $\dfrac{90}{115}$

Or,  115 s.p - 460 = 90 s.p

Or,  115 s.p - 90 s.p = 460

Or,               25 s.p = Rs 460    

∴ selling price = $\dfrac{460}{25}$ = Rs 18.4

So, The selling price of the article =s. p =  Rs 18.4

Again For gain% of 25%

i.e  gain% = $\dfrac{s.p-c.p}{c.p}$

Or, 25% = $\dfrac{s.p-c.p}{c.p}$

or,   $\dfrac{25}{100}$ = $\dfrac{s.p-c.p}{c.p}$

∴   $\dfrac{s.p}{c.p}$  = 1 + $\dfrac{25}{100}$

i.e  $\dfrac{s.p}{c.p}$ = $\dfrac{125}{100}$

∵   s.p = Rs 18.4

So,  $\dfrac{18.4}{c.p}$ = 1.25

∴  c.p = $\dfrac{18.4}{1.25}$

i.e  cost price = c.p = Rs 14.7

Hence,  The cos price of the article is Rs 14.7   Answer