The cost of a piece of diamond varies with the square of its weight. A diamond of Rs. 6,084 value is cut into 3 pieces whose weights are in the ratio 3 ∶ 2 ∶ 1. Find the loss involved in the cutting.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 2)

Answer 1

Given:

The ratio of the weight of the pieces is 3 : 2 : 1

The diamond worth Rs. 6,084 is accidentally dropped and broken into 3 pieces.

Concept used:

The cost of a piece of diamond varies with the square of its weight.

⇒ Price = k × weight²......(k is any constant)

Let the weight of a piece of the diamond be 3a + 2a + a = 6a

Calculation:

The initial value of diamond = 36ka²

According to the question,

36ka² = 6084

Then, The new value of diamond becomes = k (9a² + 4a² + a²) = 14ka²

New value of diamond = (14 × 6084)/36 = Rs. 2366

Loss occurred = 6084 - 2366 = Rs. 3718

∴ The loss involved in the cutting is Rs. 3,718.

Shortcut Trick

The initial value of diamond (3 + 2 + 1)2 = 62 = 36 unit

After cut the value becomes (32 + 22 + 12) = 14 unit,

The loss occurred (36 - 14) = 22 unit

So, 36 unit → Rs.6084

Then, 22 unit → 6084/36 × 22 = Rs.3718