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Question

Three numbers are in the ratio 2:3:4. The sum of their cube is 33957. Find the number. 


Solution

the three numbers are in the ratio 2 : 3 : 4

Hence, we can suppose the numbers as  2x,  3x  and  4x

Sum of  their cubes = (2x)³ + (3x)³ + (4x)³

By question ,

(2x)³ + (3x)³ + (4x)³ = 33957

⇒ 8x³ + 27x³ + 64x³ = 33957

⇒ 99x³ = 33957

⇒ x³ = 33957/99 = 343

⇒ (x)³  =  (7)³

Taking out the cube from both sides,

⇒ x =  7

Therefore, the numbers are:

2x = 2×7 = 14
3x = 3×7 = 21
4x = 4×7 = 28

Ans.    14, 21,  28
 

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