Question

Anil purchases two books for Rs. 100. He sells first at loss of 5% and second at 20% profit. If he gets an overall profit of 5% then what is the cost of the first book?

Answer 1

Hint – In this particular question assume any different variables be the cost of the first and second book in Rs respectively. Now the sum of the cost price is given so convert any variable in the terms of another variable so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given data:
Cost price of the two books which is purchased by the Anil is = Rs. 100
Noe let the cost of the first book be X Rs. and the cost of the second book be Y Rs.
So, X + Y = 100.
So, Y = 100 – X Rs.
Now it is given that he sells them making a loss of 5% on the first book and 20% profit on the second book.
And he earns an overall profit of 5%.
Now as we know that the percentage profit is the multiplication of the percentage of profit and the cost of the equipment.
And the percentage loss is the multiplication of the percentage of loss and the cost of the equipment.
So the sum of the loss and the profit on the first book and on the second book = (5/100) (100) = 5 Rs
Now the loss on the first book = - (5%) X, (‘-’ sign indicates the loss)
And the profit on the second book = (20%) (100 – X)
Therefore,
- (5%) X + (20%) (100 – X) = 5
Now simplify the above equation we have,
$ \Rightarrow - \dfrac{5}{{100}}X + \dfrac{{20}}{{100}}\left( {100 - X} \right) = 5$
$ \Rightarrow - 0.05X + 0.2\left( {100} \right) - 0.2X = 5$
$ \Rightarrow - 0.25X + 20 = 5$
$ \Rightarrow 0.25X = 20 - 5 = 15$
$ \Rightarrow X = \dfrac{{15}}{{0.25}} = \dfrac{{1500}}{{25}} = 60$ Rs.
So the cost price of the first book is 60 Rs.
And the cost price of the second book = (100 – 60) = 40 Rs.
So this is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that the profit on any items is the multiplication of the profit percentage and the respective cost price of the items same as for loss on any item only difference is that in loss we have to show it by a negative sign as above, so calculate the individual cost prices of the first book and the second book as above which is the required answer.