Question

Mr. Ghosh purchased wrist watches worth $Rs 60000$ . He sold one-third of them at a profit of $ 30\% $ , one third at a profit of $ 20\% $ and the remaining at loss of $5\% $. Calculate his overall profit loss percentage.

Answer 1

Hint:
This question is based on the profit and loss. When the selling price is greater than the cost price of the product then Profit happens otherwise when the cost price is greater than the selling price of the product then the Loss happens. The formula for the profit and loss is given below-
Profit = Selling Price – Cost Price
Loss = Cost Price – Selling Price
${\rm{Profit \%}} = \dfrac{{{\rm{Profit}}}}{{{\rm{Cost Price}}}} \times 100$
And, ${\rm{Loss \%}} = \dfrac{{{\rm{Loss}}}}{{{\rm{Cost Price}}}} \times 100$

Complete step by step solution
Given:
The cost price of the wrist watches ${\rm{x = Rs}}{\rm{. 60000}}$
Now according to the question,
One third of the cost price of wrist watches
$
{x_1} = \dfrac{1}{3} \times x\\
 = \dfrac{1}{3} \times 60000\\
 = 20000
$

Profit percentage earned on these watches is ${p_1} = 30\% $
The selling price of these one third watches is,
$
{{\rm{y}}_1}{\rm{ = }}{{\rm{x}}_1}{\rm{ + }}{{\rm{p}}_1}{\rm{ of }} {{\rm{x}}_1}{\rm{ }}\\
{\rm{ = }}20,000 + 30\% \times 20,000\\
 = 26,000
$

So, the profit earned on these watches is,
$
{P_1} = {y_1} - {x_1}\\
 = 26000 - 20000\\
 = 6000
$

Similarly,
One third of the cost price of another wrist watches is,
$
{x_2} = {x_1}\\
 = \dfrac{1}{3} \times x\\
 = \dfrac{1}{3} \times 60000\\
 = 20000
$

 Profit percentage earned on these watches is ${p_2} = 20\% $

The selling price of these another one third watches is,
$
{{\rm{y}}_{\rm{2}}}{\rm{ = }}{{\rm{x}}_{\rm{2}}}{\rm{ + }}{{\rm{p}}_{\rm{2}}}{\rm{ of }}{{\rm{x}}_{\rm{2}}}\\
 = 20000 + 20\% \times 20000\\
 = 24000
$

So, the profit earned on these another watches is,
 $
{P_2} = {y_2} - {x_2}\\
 = 24000 - 20000\\
 = 4000
$

And, the cost price of the remaining watches
$
{x_3} = x - \left( {{x_1} + {x_2}} \right)\\
 = 60000 - \left( {20000 + 20000} \right)\\
 = 20000
$

Loss occurred on these watches is ${l_3} = 5\% $
The selling price of these remaining watches
 $
{{\rm{y}}_{\rm{3}}}{\rm{ = }}{{\rm{x}}_{\rm{3}}}{\rm{ - }}{{\rm{l}}_{\rm{3}}}{\rm{ of }}{{\rm{x}}_{\rm{3}}}\\
 = 20000 - 5\% \times 20000\\
 = 19000
$

So, the loss occurred on these remaining watches is,
$
{{\rm{L}}_3} = {x_3} - {y_3}\\
 = 20000 - 19000\\
 = 1000
$

The, the overall profit-loss is,
$P = {P_1} + {P_2} - {L_3}$
Substituting the values, we get,
$
P = \left( {6000 + 4000} \right) - 1000\\
 = 9000
$

And we have given the total cost price $x = 60,000$
So, using the formula for the profit percentage, we have
The overall profit percentage $\% P = \dfrac{P}{x} \times 100$
Substituting the values, we get,
$
\% P = \dfrac{{9000}}{{60000}} \times 100\\
 = 15\%
$

Therefore, the overall profit-loss percentage is $15\% $.

Note:
It should be noted that in this question, the number of watches is divided into three equal parts and then we are calculating profit or loss for each part. Therefore, the overall profit-loss consists of all the values of the profit and loss for each part.