Question

2
Three numbers are in the ratio 2: 3:4. The sum of three cubes is
33957. Find the difference between the greatest and the smallest number
between the greatest and the smallest number

Answer 1

$\huge\red{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\bold{Difference \ between \ greater \ and }$

$\bold{smaller \ number \ is \ 14.}$

$\bold\orange{Given:}$

$\bold{=>Three \ numbers \ are \ in \ ratio \ of}$

$\bold{2:3:4}$

$\bold{=>Sum \ of \ their \ cube \ is \ 33957.}$

$\bold\pink{To \ find:}$

$\bold{Difference \ between \ greatest \ and}$

$\bold{smaller \ number.}$

$\bold\green{\underline{\underline{Solution:}}}$

$\bold{Let \ the \ common \ multiple \ be \ x.}$

$\bold{\therefore{Numbers \ are \ 2x, \ 3x \ and \ 4x}}$

$\bold{According \ to \ given \ condition}$

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

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

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

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

$\bold{x^{3}=343}$

$\bold{Taking \ cube \ root \ of \ both \ sides}$

$\bold{\therefore{x=7}}$

$\bold{=>Greater \ number=4x}$

$\bold{\therefore{=>Greater \ number=4×7=28}}$

$\bold{=>Smaller \ number=2x}$

$\bold{\therefore{=>Smaller \ number=2×7=14}}$

$\bold{\therefore{Difference \ between \ greater}}$

$\bold{number \ and \ smaller \ number}$

$\bold{=28-14=14}$

$\bold\purple{\tt{\therefore{Difference \ between \ greater \ and }}}$

$\bold\purple{\tt{smaller \ number \ is \ 14.}}$