Question : The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is INR 2,560. This diamond was broken down into two pieces in the ratio of 5 : 9. How much loss percentage is incurred due to this breakage? (Correct to two decimal places)
Option 1: 53.47%
Option 2: 49.71%
Option 3: 45.92%
Option 4: 55.41%

Question

Question : The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is INR 2,560. This diamond was broken down into two pieces in the ratio of 5 : 9. How much loss percentage is incurred due to this breakage? (Correct to two decimal places)

Option 1: 53.47%

Option 2: 49.71%

Option 3: 45.92%

Option 4: 55.41%

Team Careers360 · Accepted Answer

Correct Answer: 45.92%

Solution : Given: The cost of a diamond is directly proportional to the square of its weight.
A 14-gram diamond costs Rs. 2,560.
The fractured diamond pieces to total ratio is 5 : 9.
Let the diamond's cost be $k imes (weight)^2$.
⇒ $2560=k imes (14)^2$
⇒ $k=\frac{2560}{196}=13.06$
When the diamond split into two halves, 5 : 9.
Let $5x$ and $9x$ be the ratio.
This must be 14 gm.
⇒ $5x + 9x = 14$
⇒ $14x = 14$
⇒ $x = 1$
The first part = $5x=5 imes 1=5$
The second part = $9x=9 imes 1 = 9$
The cost of the first part = $13.06 imes 25$ = Rs. 326.50
The cost of the second part = $13.06 imes 81$ = Rs. 1057.86
The total cost = Rs. 326.50 + Rs. 1057.86 = Rs. 1384.36
The loss percent incurred due to this breakage = $\frac{2560–1384.36}{2560} imes 100$
$=\frac{1175.64}{2560} imes 100=45.92$%
Hence, the correct answer is 45.92%.

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Question : The cost of a piece of diamond varies with the square of its weight. A diamond of INR 6,084 value is cut into 3 pieces whose weights are in the ratio 3 : 2 : 1. Find the loss involved in the cutting.Option 1: INR 3,768Option 2: INR 3,718Option 3: INR 3,168Option 4: INR 3,518

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