Question

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

2,71,656. Find the numbers.​

Answer 1

$\huge\bold{\mathtt{Question⇒}}$

Three numbers are in the ratio $2:3:4.$ The sum of their cubes is $2,71,656.$ Find the numbers.

$\huge\bold{\mathtt{Given⇒}}$

• Three numbers are in the ratio $2:3:4.$

• The sum of their cubes is $271656.$

$\huge\bold{\mathtt{To\:find⇒}}$

The numbers.

$\huge\bold{\mathtt{Solution⇒}}$

Let the numbers are $2x,$ $3x$ and $4x.$

Sum of their cubes is $271656.$

According to condition,

$(2x)³+(3x)³+(4x)³ = 271656$

$➳\:8x³+27x³+64x³ = 271656$

$➳\:99x³ = 271656$

$➳\:x³ =({\frac{271656}{99}})$

$➳\:x³ =2744$

$➳\:x ={\sqrt[3]{2744}}$

$➳\:x ={\sqrt[3]{(14×14×14)}}$

$➳\:x =14$

$\huge\bold{\mathtt{Hence⇒}}$

$x =14$

Substitute $x$ with $14.$

• $2x =(2×14) = 28$

• $3x =(3×14) = 42$

• $4x =(4×14) = 56$

$\huge\bold{\mathtt{Therefore⇒}}$

The numbers are $28,$ $42$ and $56.$

$\huge\bold{\mathtt{Confused??}}$

$\huge\bold{\mathtt{Verification⇒}}$

$(2x)³+(3x)³+(4x)³ = 271656$

$➳\:(28)³+(42)³+(56)³ = 271656$

$➳\:(21952+74088+175616) = 271656$

$➳\:271656 = 271656$

So, L.H.S $=$ R.H.S.

Hence, verified.

$\huge\bold{\mathtt{Done}}$

• $\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

• $\large\bold{\mathtt{Enjoy\:learning\:!}}$

• $\large\bold{\mathtt{Have\:a\:nice\:day.}}$

Answer 2

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