Question

A trader purchases a watch and a wall clock for Rs. 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earns a profit of Rs. 51.50. The difference between the original prices of the wall clock and the watch is equal to?
$\left( A \right)$ Rs. 110
$\left( B \right)$ Rs. 100
$\left( C \right)$ Rs. 80
$\left( D \right)$ Rs. 120

Answer 1

Hint – In this particular question assume any variables be the cost price of the watch and the cost price of the wall clock in Rs. 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 watch and the wall clock is = Rs. 390
Noe let the cost of the watch be X Rs. and the cost of the wall clock be Y Rs.
So, X + Y = 390.
So, Y = 390 – X Rs.
Now it is given that he sells them making a profit of 10% on the watch and 15% on the wall clock.
And he earns a total profit of 51.50 Rs.
Now as we know that the percentage profit is the multiplication of the percentage of profit and the cost of the equipment.
So the sum of the profit on the watch and the wall = Rs. 51.50
Now the profit on the watch = (10%) X
And the profit on the wall clock = (15%) (390 – X)
Therefore,
(10%) X + (15%) (390 – X) = 51.50
Now simplify the above equation we have,
$ \Rightarrow \dfrac{{10}}{{100}}X + \dfrac{{15}}{{100}}\left( {390 - X} \right) = 51.50$
$ \Rightarrow 0.1X + 0.15\left( {390} \right) - 0.15X = 51.50$
$ \Rightarrow - 0.05X + 58.5 = 51.50$
$ \Rightarrow 0.05X = 58.5 - 51.5 = 7$
$ \Rightarrow X = \dfrac{7}{{0.05}} = 140$ Rs.
So the cost price of the watch is 140 Rs.
And the cost price of the wall clock = (390 – 140) = 250 Rs.
Now the difference of the original prices of the wall clock and the watch is
Therefore, (250 – 140) = 110 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, so first calculate the individual cost prices of the watch and the wall clock then subtract the lower cost price from the higher cost price as above we will get the required answer.