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.

• How do you define profit percentage? If you buy a thing for $C$ and sell it for $S$ do you look at $\frac {S-C}C$ or $\frac {S-C}S$? – lulu Sep 2 '16 at 14:04
• @lulu It's obviously (S-C)÷C. – Omkar Reddy Sep 2 '16 at 14:12
• Well, I don't think it's obvious. Both have some good features. Regardless, I'll post a calculation below. – lulu Sep 2 '16 at 14:14

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 $$P_3=.85\times \frac {P_2+1}{.65}-1=\frac {17}{13}P_2+\frac 4{13}$$

• That's ok. But here we need to calculate change in the profit percentage. – Omkar Reddy Sep 2 '16 at 14:19
• So? You want $P_3-P_2=\frac 4{13}P_2+\frac 4{13}=\frac 4{13}\times (P_2+1)$, yes? – lulu Sep 2 '16 at 14:27
• Yes, I think so. This is little ambiguous. It might be (P3-P2)÷P2. The answer was given as 30.76%. But I can't understand. – Omkar Reddy Sep 2 '16 at 14:35
• I note that $\frac 4{13}=30.76\%$ so I expect that what I wrote is, more or less, what was intended. – lulu Sep 2 '16 at 14:37
• Ok, I also knew that but there is unknown term on the right side of the equation. How could you eliminate that? – Omkar Reddy Sep 2 '16 at 14:42

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

• This is wrong method. How could you consider Selling price as Cost price? Without knowing the actual cost how could you calculate change in the percentage profit? So, do you mean profit percentage is independent of CP? What is the source of this method? For Different values of Cost price you'll get different values of percentage profit change. See the below answer once. I think we can't solve this since the data is insufficient. – Omkar Reddy Sep 22 '16 at 18:58

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.