If three numbers are in the ratio 3 : 4 : 5 such that the sum of their cubes is 1728

If three numbers are in the ratio 3 : 4 : 5 such that the sum of their cubes is 1728, then the cube of the middle number is

  1. 216
  2. 512
  3. 256
  4. 128
Anurag Mishra Professor Asked on 19th April 2016 in Maths.
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1 Answer(s)

Answer: (2) 512

Solution:-
The ratio of three numbers = 3: 4: 5.
Then, let three number be 3 X, 4 X and 5 X

The sum of their cubes is 1728,
Then, (3 X)3 + (4 X)3 + (5 X)3 = 1728
27 X3 + 64 X3 + 125 X3 = 1728
216 X3 = 1728
X3 = 1728/216
X3 = 8
Cube root on both side,
X = 2

The middle number = 4 X = 4 x 2
= 8

So, the cube of 8 = 8 x 8 x 8
= 512

Hence, the correct answer is option (2) 512.

Anurag Mishra Professor Answered on 20th April 2016.
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