Question

ITC sells one product at a profit of 20% another at a loss of 20% at the same selling price. What is the loss incurred by ITC?

A) 1% B) 2% C) 4% D) 0%

Answer 1

$\sf\large\underline{Let:}$

$\tt{\implies The\: selling\: price\:of\: the\:product=100}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies Loss\: incurred\:by\:ITC=?}$

$\sf\large\underline{Given\:in\:the\: Question:}$

$\tt{\implies Profit\:on\:1st\: product=20\%}$

$\tt{\implies Loss\:on\:2nd\: product=20\%}$

• Now calculate the cost price of each product separately than calculate total selling price and cost price of the product and at last calculate loss%]

$\sf\large\underline{Formula\: used:}$

$\tt{\implies CP=\dfrac{100}{100+G\%}\times\:SP}$

$\tt{\implies CP\:_{(product\:1st)}=\dfrac{100}{100+20}\times\:100}$

$\tt{\implies CP\:_{(product\:1st)}=\dfrac{100}{120}\times\:100}$

$\tt\red{\implies CP\:_{(product\:1st)}=\dfrac{1000}{12}}$

$\tt{\implies CP\:_{(product\:2nd)}=\dfrac{100}{100-L\%}\times\:SP}$

$\tt{\implies CP\:_{(product\:2nd)}=\dfrac{100}{100-20}\times\:100}$

$\tt{\implies CP\:_{(product\:2nd)}=\dfrac{100}{80}\times\:100}$

$\tt\green{\implies CP\:_{(product\:2nd)}=\dfrac{1000}{8}}$

• Now calculate total CP and SP ,here]

$\tt{\implies Total\:_{(CP)}=CP\:_{1st}+CP\:_{(2nd)}}$

$\tt{\implies Total\:_{(CP)}=\dfrac{1000}{12}+\dfrac{1000}{8}}$

$\tt{\implies Total\:_{(CP)}=\dfrac{2000+3000}{24}}$

$\tt{\implies Total\:_{(CP)}=\dfrac{5000}{24}}$

$\tt\purple{\implies Total\:_{(CP)}=\dfrac{625}{3}}$

$\tt{\implies Total\:_{(SP)}=SP\:_{1st}+SP\:_{(2nd)}}$

$\tt{\implies Total\:_{(SP)}=100+100}$

$\tt\orange{\implies Total\:_{(SP)}=200}$

• Now calculate total loss , here]

$\tt{\implies Total\:_{(Loss)}=Total\:_{(CP)}-Total\:_{(SP)}}$

$\tt{\implies Total\:_{(Loss)}=\dfrac{625}{3}-200}$

$\tt{\implies Total\:_{(Loss)}=\dfrac{625-600}{3}}$

$\tt\green{\implies Total\:_{(Loss)}=\dfrac{25}{3}}$

• For final answer calculate loss%]

$\tt{\implies Total\:_{(Loss\%)}=\dfrac{100\times\:Loss}{CP}}$

$\tt{\implies Total\:_{(Loss\%)}=\dfrac{100\times\:25/3}{625/3}}$

$\tt{\implies Total\:_{(Loss\%)}=\dfrac{100}{25}}$

$\tt\blue{\implies Total\:_{(Loss\%)}=4\%}$

$\sf\large{Hence,}$

$\bf\purple{\implies Loss\: incurred\:by\:ITC=4\%}$

$\tt{\underbrace{ANSWER:-OPTION-(C)}}$