Question

A trader used to make $5\%$ profit on an item selling at usual marked price. One day, he trebled the marked price of the item and finally offered a discount of $30\%$. Find the percentage profit he made on the item that day.

• A. Rs.8
• B. Rs.9
• C. Rs.10
• D. Rs.12

Answer 1

The correct option is D

Rs.12

Method 1: Conventional approach
Cost of a tubelight = Rs. t and cost of a bulb = Rs. b
t + b = 52
Cost of bulb drops by 20% and cost of tubelight increases by $50\%$
Therefore, 1.5t + 0.8b = 50
Solving the two equations in 't' and 'b',
t + b = 52
1.5t + 0.8b = 50
Multiplying first equation by 4 and second equation by 5,
4t + 4b = 208
7.5t + 4b = 250
Subtracting,
3.5t = 42
Hence, t = 12
Thus, cost of a tubelight = Rs. 12
Shortcut!- Reverse Gear

Checking for option (c)

$\begin{array}{ccc}Tubelight& 10& 15\\ Bulb& 42& 33\\ & 52& 48\end{array}$

From this we can deduce that the cost of the tubelight is very close to our assumption. We can also directly mark option (d) as the correct answer without verifying because with a Rs.10 tubelight we are getting the new cost as Rs.48 ; thus the cost of the tubelight has to be slightly more than Rs.10 to get the cost of the package as Rs.50 !