Dark Mode

Akash Kanase
asked
in Quantitative Aptitude
Feb 16, 2016

6,819 views
9 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.

- $5$
- $10$
- $15$
- $30$

8 votes

Best answer

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: $A$

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: $A$

0

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.**

3

9 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 %

4 votes

$SP-CP=Profit$

$SP-100=500$

$SP=600$

$Cost\ of\ Product=60/unit$

$\#\ of\ Products=10$

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

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

$But\ Profit\ remains\ same$

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

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

$10\times x-130=500$

$x=63$

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

**$Ans\ is\ 5$**