Question

The value of a gold bar is directly proportional to the square of its weight. If a gold bar weighing 8 kg breaks into 2 pieces, its total value decreases by $\frac{3}{8}$ times. Find the weights of the two pieces.

• A. 4 kg, 4 kg
• B. 5 kg, 3 kg
• C. 6 kg, 2 kg
• D. 4.5 kg, 3.5 kg

Answer 1

The correct option is C

6 kg, 2 kg

Value (V) = K $\times 8^2$ = 64 K

Let weights be x kg and (8 - x) kg.

V1 = K$x^2$ and V2 = $K(8-x{)}^2$

New value = $K[x^2+(8-x{)}^2]$

Given $K[x^2+(8-x{)}^2]=\frac{5}{8}(64k)$
$x^2+64+x^2-16x=40$

$2x^2-16x+24=0$

$x^2-8x+12=0\Rightarrow (x-6)(x-2)=0$

x = 6, x = 2.

Alternatively :

Assume k=1; the solution becomes simpler.
Value is currently 64 and it becomes ${\frac{5}{8}}^{th}$ of that which is 40 =36+4 (This is the only possible breakup with 2 square numbers) hence, answer is option (c).