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28 Sep 2025, 23:31
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:35) correct
41%
(02:45)
wrong
based on 104
sessions
History
Date
Time
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Not Attempted Yet
A precious stone worth $10872 fell and broke into three pieces, the weights of which are proportional to 1 : 2 : 3. The value of each stone is directly proportional to the square of its weight. What is the loss in the value caused by the breakage?
(A) $3624
(B) $4228
(C) $6644
(D) $7510
(E) $8980
(A) $3624
(B) $4228
(C) $6644
(D) $7510
(E) $8980
29 Sep 2025, 00:27
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Let the weight broken stones be x, 2x & 3x
That means, total weight should be 6x before it broke down
Total value of stone before it broke down should be
(6x)^2 * k = 10872
where k is proportionality constant
36x^2 * k = 10872
x^2 * k = 302
Now values of broken pieces will be x^2, 4x^2, 9x^2 (squaring each weight)
Total value of pieces = 14x^2
And we just calculated that x^2 * k = 302
Therefore, Total value of pieces = 14*302 = 4228
Hence, the loss in the value caused by the breakage = 10872 - 4228 = $6644
That means, total weight should be 6x before it broke down
Total value of stone before it broke down should be
(6x)^2 * k = 10872
where k is proportionality constant
36x^2 * k = 10872
x^2 * k = 302
Now values of broken pieces will be x^2, 4x^2, 9x^2 (squaring each weight)
Total value of pieces = 14x^2
And we just calculated that x^2 * k = 302
Therefore, Total value of pieces = 14*302 = 4228
Hence, the loss in the value caused by the breakage = 10872 - 4228 = $6644
29 Sep 2025, 04:56
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Bunuel
Before Breaking , the total weight = x + 2x + 3x = 6x
Value is proportional to the square of the weight.
Value = k . (Weight)^2
$10872 = k . (6x)^2
$10872 = k . 36x^2
(10872/36) = k. x^2
302 = k. x^2
After Breaking
weights are in the ratio : x:2x:3x
weight squares ratio = x^2 : 4x^2 : 9x^2
Sum of the weight squares = ( x^2 + 4x^2 + 9x^2 ) = 14x^2
The new value = 14 * (k x^2)
= 14 * 302
= 4228.
Value lost = $10872 - $4228
= $ 6,644.
Option C
