Could you please help me solve this problem of profit and loss?

Question

A shopkeeper changes the discount on marked price of an article from 35% to 15%. Find the change in profit percentage?

It seems that the data is insufficient but answer was given something else.

I couldn't' understand how it's possible.

Please help me solve this problem.

Answer 1

Suppose the shopkeeper's cost was $C$. Then there are three sales prices to consider: $S_1$, the original price. $S_2$ the price after a $35\%$ discount. And $S_3$, the price after a $15\% $ discount. In each case we define $P_i$ to be the associated profit percentage : $P_i=\frac {S_i-C}{C}$. You are asked to compare $P_2$ and $P_3$.

We easily see that $S_2=.65\,S_1$ and $S_3=.85\,S_1$ whence we conclude that $$P_2=.65\frac {S_1}C-1\;\;\;\&\;\;\;P_3=.85\frac {S_1}C-1$$ It follows that $$P_3=.85\times \frac {P_2+1}{.65}-1=\frac {17}{13}P_2+\frac 4{13}$$

Answer 2

you need to understand what is being askd here, it is asking for profit change and not the exact profit.. let me explain

assume the markup price be of 100 (for simplicity)

now in case 1 , 35% discount is offered, which means article sells at 65

case 2 discount CHANGED to 15%, so new price of article is 85..

now the value change here wrt to the case1 price will give us % change (which will be same as profit CHANGE we need to calculate),

in simple terms we treat 65 as cost price and 85 as selling price

(85-65)/65 = 30.76

Answer 3

It's an easy question . If a shopkeeper made a discount of 35% to 15% that means he increased the price of the article 20% ( 35 - 15 = 20 ) or made a profit of 20 % more.

Cost price = 100%

Selling price = 65% ( 35 percent discount )

Loss = 35% discount

THEN

Cost price = 100%

Selling price = 85 %

Loss = 15%

So, the profit from 85% to 65% ( 35% to 15% )is 20% the shopkeeper made.

Answer = 20% profit