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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. $30$

what does same profit level mean .. is it same profit percentage or same profit amount ?
Official answer key shows it is 5%. I think they are talking about the same profit amount.

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: $A$

Why is this key  not reviewed??

Here profit level should be same.  That means, profit percent should same as previous.

Am I missing something?

@srestha

it is given that 30% of the cost is increased, so now it has become 130

Now it is asked for, by what % the selling price must increase to maintain the same profit. See previously we have profit of 500, so now to preserve the same profit we need to sell it in 500+130 = 630

Now, 600+ (x/100)*600 =630

from here we get x= .05

i.e 5% increase.

PLEASE NOTE THAT WE ARE ASKED FOR WHAT % INCREASED IN SELLING PRICE.

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 %

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

$SP-CP=Profit$

$SP-100=500$

$SP=600$

$Cost\ of\ Product=60/unit$

$\#\ of\ Products=10$

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

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

$But\ Profit\ remains\ same$

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

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

$10\times x-130=500$

$x=63$

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

$Ans\ is\ 5$