Question

A man bought $ 3 $ toffees for a rupee. How many for a rupee he will sell to gain $ 50\% $ ?
A. $ 2 $
B. $ 3 $
C. $ 4 $
D. $ 1 $

Answer 1

Hint: Selling price is the sum of cost price and profit. Calculate the selling price of three toffees to understand how many toffees should be sold for a rupee.

Complete step-by-step answer:
In this question it is given that a man bought 3 toffees for a rupee
He wants to make a profit of $ 50\% $ .
According to the question.
Cost price of \[3\]toffees $ = $ ₹ $ 1 $
Now we have to find $ 50\% $ profit on ₹ 1
We have formula for profit percentage as
 $ Profit\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 $
Where,
S.P. is the selling price
C.P. is the cost price
By substituting the given information in above formula, we get
 $ 50 = \dfrac{{S.P. - 1}}{1} \times 100 $
By rearranging it, we get
 $ S.P. - 1 = \dfrac{{50}}{{100}} $
 $ \Rightarrow S.P. - 1 = \dfrac{1}{2} $
 $ \Rightarrow S.P. = \dfrac{1}{2} + 1 $
By cross multiplying, we get
 $ \Rightarrow S.P. = \dfrac{{1 + 2}}{2} $
 $ \Rightarrow S.P. = \dfrac{3}{2} $
Hence, selling price of 3 toffees is ₹ $ \dfrac{3}{2} $
Therefore, selling price of 1 toffees will be $ \dfrac{3}{2} \times \dfrac{1}{3} = $ ₹ $ \dfrac{1}{2} $
Therefore, selling price of 2 toffees will be $ 2 \times \dfrac{1}{2} = $ ₹ $ 1 $
Hence, he should sell 2 toffees per rupee to gain $ 50\% $
Therefore, from the above explanation, the correct answer is, option (A) $ 2 $

So, the correct answer is “Option A”.

Note: We can solve this question smartly just by looking at the options.
He can’t sell 3 toffees for a rupee as that is his cost price and he will not gain any profit.
If he sells 4 toffees for a rupee then he will be in loss because he is buying 3 toffees at the same price.
If he sells 1 toffee for a rupee then that will be 3 times his cost price and he will make more than $ 50\% $ profit.
Therefore, option (B), (C), (D) are incorrect.
Hence, correct answer must be option (A) $ 2 $