# Clarification on language of a question on profit and loss.

The question is:

By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.

1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%

The answer provided by the book says it's the first one.

But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think

(11/22) * 100

The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.

The question might be wrong and that is why I am seeking help.

• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? – shardulc says Reinstate Monica Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay. – lulu Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. – vickyace Aug 17 '16 at 18:15

This question is (perhaps intentionally) poorly worded, so it may help to convert everything into dollars: assume each meter costs him $\$1$. Then, when selling 33 meters, which costs him$\$33$, the shopkeeper gains "the cost of 11 meters" or, $\$11$. That is, on an investment of$\$33$, the shopkeeper gains $\$11$. The "gain percentage" is then simple$\frac{\$11}{\$33} = 33.3\%\$.