Question

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

Answer 1

.Let the no be 2x , 3x ,4x
sum of their cubes=
8x^3+27x^3+64x^3=33957
99x^3=33957
x^3=33957/99
x^3=343
x =cube root (343)
x=7
Therefore,the no are:
2×7=14
3×7=21
4×7=28

Hope it helps!!!!

Answer 2

Let the no. be 2x , 3x and 4x

According to question

$(2x) {}^{3} +( 3x) {}^{3} + (4x) {}^{3} = 33957$

$8x {}^{3} + 27x {}^{3} + 64x {}^{3} = 33957$

$99x {}^{3} = 33957$

$x {}^{3} = \frac{33957}{99}$

$x = \sqrt[3]{343}$

$x = 7$

Therefore, the numbers are

2x =2×7

= 14

3x = 3×7

= 21

4x= 4×7

= 28

So, the numbers are 14, 21 and 28