Question

An article is sold at 20% profit. If its cost price is increased by Rs.50 and at the same time, if its selling price is also increased by Rs 30, the percentage of profit decreases by $\dfrac{{10}}{3}\% $. Find the cost price approximately.
A. 500
B. 850
C. 700
D. 800

Answer 1

Hint: Profit and loss percentages are used to refer to the amount of profit or loss that has been incurred in terms of percentage.
Cost Price (C.P.): Price at which an article is purchased.
Selling Price (S.P.): Price at which an article is sold by a shopkeeper.
If the selling price is more than cost price then it is known as profit.
$Profit = S.P.({\text{Selling price}}) - C.P.({\text{Cost price}})$
If the selling price is less than cost price then it is known as loss.
$Loss = C.P.({\text{ Cost price}}) - S.P.({\text{Selling price}})$
Profit percentage is calculated on cost price.
$Profit\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$
Loss percentage is calculated on cost price.
$Loss\% = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100$
$S.P. = C.P\left( {\dfrac{{100 + \% Profit}}{{100}}} \right)

Complete step by step solution:
Let the cost price be Rs x
It is sold at 20% profit
$
  \therefore S.P. = C.P.\left( {\dfrac{{100 + \% Profit}}{{100}}} \right) \\
  S.P. = x\left( {\dfrac{{100 + 20}}{{100}}} \right) \\
  S.P. = \dfrac{{12}}{{10}}x \\
$
New cost price = $Rs(x + 50)$
New selling price = $Rs\left( {\dfrac{{12x}}{{10}} + 30} \right)$
New profit = $S.P. - C.P.$
$ = \left( {\dfrac{{12x}}{{10}} + 30} \right) - \left( {x + 50} \right)$
$
   = \dfrac{{12x - 10x}}{{10}} + 30 - 50 \\
   = \dfrac{{2x}}{{10}} - 20 \\
$
$
  \therefore \% Profit = \left( {\dfrac{{Profit}}{{New{\text{ }}C.P.}}} \right) \times 100 \\
  \left( {20 - \dfrac{{10}}{3}} \right)\% = \left( {\dfrac{{\dfrac{{2x}}{{10}} - 10}}{{x + 50}}} \right) \times 100 \\
  \dfrac{{50}}{3} = \dfrac{{\left( {2x - 200} \right) \times 10}}{{x + 50}} \\
  50\left( {x + 50} \right) = 30\left( {2x - 200} \right) \\
  50x + 2500 = 60x - 6000 \\
  60x - 50x = 6000 + 2500 \\
  10x = 8500 \\
  x = Rs850 \\
$
∴Option (B) is correct.

Note:
This type of question can be solved by taking the cost price Rs 100. The main step in this question is to find a new cost price and new selling price. Finally here we have to compare new profit% with old profit%. For profit, the selling price should be more than the cost price while for loss, cost price should be more than the selling price.
On selling an article for Rs. x, a person earns a% profit. In order to earn b% profit, he must sell the article for Rs. $\dfrac{{x \times \left( {100 + b} \right)}}{{\left( {100 + a} \right)}}$.
When there is a profit of x% and loss of y% then net percentage profit or loss =$\left[ {\dfrac{{x - y - xy}}{{100}}} \right]$ and if the final sign in this expression is positive then there is net profit but if it is negative then there is net loss.