Question

A shopkeeper at Ganga sells an
item at a certain price. If he sells that
item at 33.33% of the original selling
price, then he suffers a loss of 33.33 %.
Find the profit percent, if he sells that
item at 60% of the original selling
price?​

Answer 1

Given :

The item sold at 33.33% of the original selling  price, then he suffers a loss of 33.33 %.

To Find :

The profit percent, if  item sold at 60% of the original selling  price

Solution :

Let The original selling price = Rs s.p

Let The cost price of item = Rs c .p

∵ The item sold at 33.33% of the original selling  price

i.e  $s.p_2$ = 33.33 % of s.p

Or, $s.p_2$ = 0.3333 × s.p

∵ Loss % = $\dfrac{cost price - selling price}{cost price}$

Or,  33.33 % = 1 - $\dfrac{s.p_2}{c.p}$

Or, $\dfrac{s.p_2}{c.p}$ = 1 - 33.33 %

Or, $\dfrac{0.3333 s.p}{c.p}$ = 1 - 0.3333

Or,   $\dfrac{s.p}{c.p}$   = $\dfrac{0.6667}{0.3333}$                .............1

Again

When he sells that  item at 60% of the original selling  price

So,   $s.p_3$ = 60 % of s.p

Or, $s.p_3$ = 0.6 × s.p

∵ profit % = $\dfrac{selling price - cost price}{cost price}$

Or,            =  $\dfrac{s.p_3}{c.p}$ - 1

Or,            =  $\dfrac{0.6 s.p}{c.p}$ - 1

Or,            = 0.6 × $\dfrac{s.p}{c.p}$ - 1

Or,           =  0.6 ×  $\dfrac{0.6667}{0.3333}$  - 1                           ( from eq 1 )

∴              = 0.20

i.e Profit % = 20

Hence, The profit percentage when item sold at 60% of the original selling  price is 20 %   . Answer