Question

A trader purchases a watch and a wall clock of 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

• A. Rs. 110
• B. Rs. 100
• C. Rs. 80
• D. Rs. 120

Answer 1

The Correct Option is A

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,
⇒ \(\frac{10}{100}X+\frac{15}{100}(390-X)=51.50\)
⇒ \(0.1X+0.15(390)-0.15X=51.50\)
⇒ \(-0.05X+58.5=51.50\)
⇒ \(0.05X=58.5-51.5=7\)
⇒ \(X=70.05=140\)
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.
The correct option is (A): Rs. 110