Question

Three numbers are to one another 2:3:4. The sum of their cube is 33957. Find the numbers

Answer 1

Let the number be 2x,3x and 4x.
A.T.Q.
2x+3x+4x=33957
=>9x=33957
=>x=33957÷9
=>x= 3773
Now, the numbers are
2×3773 = 7546
3×3773 =11319
4×3773 =15092
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Answer 2

Let the nos. be 2x, 3x, 4x
Acc. to ques. => (2x)³+(3x)³+(4x)³ = 33957
=> 8x³+27x³+64x³ = 33957
=> 99x³ = 33957
=> x³ = 33957/99
=> x³ = 343
=> x = ³√343
=> x = 7
Therefore the nos. are --
2x = 2×7 = 14
3x = 3×7 = 21
4x = 4×7 = 28


For cross-check --
14:21:28 = 2:3:4
and sum of cubes --
(14×14×14)+(21×21×21)+(28×28×28) = 2744 + 9261 + 21925 = 33957


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