Question

The price of a diamond is directly proportional to square its weight. A trader bought a piece of diamond weighing 10 grams for Rs.2,00,000. He broke it into three pieces of weights 5 grams, 3 grams and 2 grams, and sold them individually. What was the total loss incurred by the trader?

• A. No loss
• B. Rs.1,24,000
• C. Rs.1,00,000
• D. Rs.76,000

Answer 1

The Correct Option is B

Diamond Price Calculation and Loss 

Step 1: Understanding the Proportionality Rule

The price of the diamond is directly proportional to the square of its weight:

\[ P = k \times W^2 \]

Step 2: Finding the Constant of Proportionality (k)

Given the price of the 10-gram diamond is Rs. 2,00,000:

\[ 2,00,000 = k \times 10^2 \] \[ k = \frac{2,00,000}{100} = 2000 \]

Step 3: Calculating the Prices of Broken Pieces

• Price of the 5-gram piece: \[ P_5 = 2000 \times 5^2 = 2000 \times 25 = 50,000 \]
• Price of the 3-gram piece: \[ P_3 = 2000 \times 3^2 = 2000 \times 9 = 18,000 \]
• Price of the 2-gram piece: \[ P_2 = 2000 \times 2^2 = 2000 \times 4 = 8,000 \]

Step 4: Calculating the Total Price After Breaking

Total price after breaking the diamond:

\[ Total \ Price = 50,000 + 18,000 + 8,000 = 76,000 \]

Step 5: Calculating the Loss

The trader bought the diamond for Rs. 2,00,000 and sold the pieces for Rs. 76,000. The total loss is:

\[ Loss = 2,00,000 - 76,000 = 1,24,000 \]

Step 6: Conclusion

The total loss incurred by the trader is Rs. 1,24,000.