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10 votes
10 votes

A firm is selling its product at Rs. $60$ per unit. The total cost of production is Rs. $100$ and firm is earning total profit of Rs. $500$. Later, the total cost increased by $30\%.$ By what percentage the price should be increased to maintained the same profit level.

  1. $5$
  2. $10$
  3. $15$
  4. $30$

8 Answers

Best answer
9 votes
9 votes
Let $N$ units be made.

Selling price per item $=Rs. 60$

Let $X$ be the cost per unit

We are given

$500 (\text{as profit}) =\underbrace{60-X +60-X+60-X +60-X + \dots 60-X}_{N\; times}$

$N(60-X)=500\implies 60N-NX=500$

Total cost is $Rs. 100 \implies  (60N-100)=500\implies N=10$

Now the cost has increased by $30\%$

New cost is $Rs.130$ and the extra $30$ has to be equally divided among $10$ units to maintain same profit level.

So, selling price should increase by $3$ from $60$ $\implies$ $\frac{3}{60} \times{100} = 5\%$ increase.

Correct Answer: $A$
edited by
11 votes
11 votes

Selling price per unit = Rs. 60

Total Cost Price of production = Rs. 100

Total profit  = Rs. 500

Total Selling Price  = Total CP + Total profit = Rs. ( 500 + 100 )  = Rs. 600

Now, Number of units sold = Total SP / (SP of one unit )  = 600 / 60  = 10 units


Now total cost increased by 30% 

So, the new Total CP becomes    100 + 30% of 100  = Rs. 130

Now, I considered  profit level as two possible meanings -  same profit %  or same total profit amount 


Case (i) - Same profit percentage -

                Old profit percent  =    $\frac{500}{ 100}$  * 100   = 500 %

 ​                New  Total CP  = Rs. 130

                          profit   = 500 % of 130  =Rs.  650 

                        Total price (SP) = Rs. (130 + 650) = Rs. 780

                          percentage increase in price =   $\frac{New SP - Old SP}{ Old SP} * 100$                        

                                                                         =     $\frac{780 - 600}{ 600} * 100$

                                                                         =     30 %


Case(ii)  - If I consider same profit amount -

                    Total CP(new) = Rs. 130

                    Total profit  = Rs. 500

                    New Total SP = Rs.  630

                     %age  increase in price(SP) = $\frac{New SP - Old SP}{ Old SP} * 100$

                                                                   =   $\frac{630 - 600}{ 600 } * 100$

                                                                   =  5 %

6 votes
6 votes

No. of items sold initially=600/60=10

with 30% increase in total cost, selling price for each product=630/10=63

increase in selling price=63-60=3

i.e 5% of initial selling price

4 votes
4 votes

$SP-CP=Profit$

$SP-100=500$

$SP=600$

$Cost\ of\ Product=60/unit$

$\#\ of\ Products=10$


$Cost\ of\ Production\ increased\ by\ 30\%$

$CP_{new}=100+\dfrac{30}{100}\times100=130$

$But\ Profit\ remains\ same$

$\therefore SP_{new}-CP_{new}=500$

$\#\ of\ Products\times cost\ of\ Product-130=500$

$10\times x-130=500$

$x=63$


$\%\ increase=\dfrac{63-60}{60}\times 100=5$

$Ans\ is\ 5$

Answer:

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