Determining Ram's Watch Profit Percentage

This question asks us to calculate the total profit or loss percentage Ram experienced. We need to find out how much profit he made relative to the price he actually paid for the watch.

Step 1: Calculate Ram's Purchase Cost

First, let's establish a baseline for the watch's cost. We can assume the Original Cost (OC) is 100 units. Ram bought the watch for $\frac{9}{10}^{th}$ of this amount.

Ram's actual Purchase Cost (CP) is calculated as:

CP = $\frac{9}{10} \times \text{Original Cost}$

If OC = 100, then:

CP = $\frac{9}{10} \times 100 = 90$ units.

Step 2: Calculate Ram's Selling Price

Next, we determine the price Ram sold the watch for. He sold it for 8% more than the Original Cost.

Selling Price (SP) = Original Cost + (8% increase on Original Cost)

SP = $OC + ( \frac{8}{100} \times OC )$

Using OC = 100:

SP = $100 + ( \frac{8}{100} \times 100 ) = 100 + 8 = 108$ units.

Step 3: Calculate the Profit Amount

Profit is the difference between the selling price and the cost price Ram paid.

Profit = Selling Price (SP) - Purchase Cost (CP)

Profit = $108 - 90 = 18$ units.

Since the selling price (108) is higher than the purchase cost (90), Ram made a profit.

Step 4: Calculate the Profit Percentage

The profit percentage is calculated based on the price Ram actually paid (his Purchase Cost, CP).

Profit Percentage = $ ( \frac{\text{Profit}}{\text{Purchase Cost (CP)}} ) \times 100 $

Profit Percentage = $ ( \frac{18}{90} ) \times 100 $

Simplify the fraction:

Profit Percentage = $ ( \frac{1}{5} ) \times 100 $

Profit Percentage = $20\%$

Result: Ram's Gain

Ram made a 20% profit on the watch.