Question

A person X buys pens and pencils at Rs. 5 and Rs. 1 per piece respectively. For every two pens, he buys three pencils. He sold pens and pencils at 12% and 10% profit respectively. If his total sale is Rs 725, then the number of pencils exceeds the number of pens by
A. 25
B. 50
C. 75
D. 90

Answer 1

Hint: If an item costs Rs x and person sells it at profit of y% then selling price of that item will be x + \[\dfrac{{\text{y}}}{{{\text{100}}}}{\text{*x}}\] = Rs x*\[\left( {\dfrac{{{\text{100 + y}}}}{{{\text{100}}}}} \right)\].

Complete step-by-step answer:
As it is given in question that cost of per piece of pencil is Rs 1.
And profit per piece of pencil is 10%.
So, cost of one pencil including profit will be Rs 1*\[\left( {\dfrac{{{\text{100 + 10}}}}{{{\text{100}}}}} \right)\] = Rs 1*1.1 = Rs 1.1.
As it is given in the question that the cost of one pen is Rs 5.
And profit per piece of pen is 12%.
So, cost of one pen including profit will be Rs 5*\[\left( {\dfrac{{{\text{100 + 12}}}}{{{\text{100}}}}} \right)\] = Rs 5*1.12 = Rs 5.6.
As it is given in the question that the person X buys 3 pencils for every 2 pens.
Let each pair include 3 pencils and 2 pens.
So, cost for 3 pencils and 2 pens (1 pair) including profit will be Rs (3*1.1 + 2*5.6) = Rs 14.5
And it is given that the total sale of person X is Rs 725.
So, the number of pairs person X has sold will be equal to the total sale divided by the selling cost of one pair.
So, total pairs person X had sold = \[\dfrac{{725}}{{14.5}}\] = 50.
As we know that in one pair there are 2 pens and 3 pencils.
So, the number of pens person X had bought will be equal to two times the number of pairs person X had sold.
So, number of pens person X had brought will be 2*50 = 100.
And, the number of pencils person X had bought will be equal to three times the number of pairs person X had sold.
So, number of pencils person X had brought will be 3*50 = 150.
So, number of pencils exceeds number of pens by 150 – 100 = 50
Hence, the correct option will be B.

Note: Whenever we come up with this type of problem then first, we find the total profit on each pair. And then after that we will find the selling price of person X for each pair. After that we can divide the total sale price with the selling price of one pair to get the number of pairs sold. After that we can easily get the number of pens and pencils by multiplying the number of pairs with the number of pens or pencils in one pair. After then we subtract that to get by how much quantity the pencil exceeds the pens.