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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