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 38 times. Find the weights of the two pieces.
Answer: Option C
:
C
Value (V) = K ×82 = 64 K
Let weights be x kg and (8 - x) kg.
V1 = Kx2 and V2 = K(8−x)2
New value = K[x2+(8−x)2]
Given K[x2+(8−x)2]=58(64k)
x2+64+x2−16x=40
2x2−16x+24=0
x2−8x+12=0⇒(x−6)(x−2)=0
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:
C
Value (V) = K ×82 = 64 K
Let weights be x kg and (8 - x) kg.
V1 = Kx2 and V2 = K(8−x)2
New value = K[x2+(8−x)2]
Given K[x2+(8−x)2]=58(64k)
x2+64+x2−16x=40
2x2−16x+24=0
x2−8x+12=0⇒(x−6)(x−2)=0
x = 6, x = 2.
Alternatively :
Assume k=1; the solution becomes simpler.
Value is currently 64 and it becomes 58th of that which is 40 =36+4 (This is the only possible breakup with 2 square numbers) hence, answer is option (c).
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