Question

A shopkeeper sold goods for ₹1800 and made a profit of 20% in the process. Find his profit per cent if he has sold his goods for ₹ 1687.5.

Answer 1

Given :

Selling price : ₹1800

Profit percentage : 20%

To find :

Profit percentage if sold at ₹1687.5.

Solution :

First, we should find the cost price of the goods.

Cost price of the goods :

$\sf \dashrightarrow \dfrac{100}{(100 + Profit\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 + 20)} \times 1800$

$\sf \dashrightarrow \dfrac{100}{120} \times 1800$

$\sf \dashrightarrow \dfrac{5}{6} \times 1800$

$\sf \dashrightarrow \dfrac{5 \times 1800}{6} = \dfrac{9000}{6}$

$\sf \dashrightarrow \cancel \dfrac{9000}{6} = 1500$

Now, we should find the new profit rupees of the goods.

New profit rupees :

$\sf \dashrightarrow Selling \: price - Cost \: price$

$\sf \dashrightarrow 1687.5 - 1500$

$\sf \dashrightarrow Rs.187.5$

Now, we can find the profit percentage.

New profit percentage :

$\sf \dashrightarrow \dfrac{Profit}{Cost \: price} \times 100$

$\sf \dashrightarrow \dfrac{187.5}{1687.5} \times 100$

$\sf \dashrightarrow \dfrac{1}{9} \times 100$

$\sf \dashrightarrow \dfrac{1 \times 100}{9} = \dfrac{100}{9}$

$\sf \dashrightarrow \cancel \dfrac{100}{9} = 11.11$

Hence, the new profit percentage of the goods is 11.11%.

Answer 2

Answer:

Step-by-step explanation:

sp=1800

profit= 20%

so, cp=sp/1+profit

cp=1800/1+0.2

cp=1500

new, sp=1687.5

profit=(sp/cp)-1

profit=1687.5/1500)-1

profit=1.125-1

profit%=0.125

           =0.125*100

           =12.5%