Question

two numbers are in ratio 3:4. If the difference of their cubes is 999 find the numbers​

Answer 1

$\huge\bold{\mathbb{QUESTION}}$

Two numbers are in ratio $3:4.$ If the difference of their cubes is $999,$ find the numbers.

$\huge\bold{\mathbb{GIVEN}}$

• Ratio $= 3:4$

• Difference of their cubes $= 999$

$\huge\bold{\mathbb{TO\:FIND}}$

The numbers.

$\huge\bold{\mathbb{SOLUTION}}$

Let the numbers are $3x$ and $4x$ respectively.

Difference of their cubes $= 999$

So, we can say-

$(4x)^{3}-(3x)^{3} = 999$

$\implies 64x^{3}-27x^{3}= 999$

$\implies 37x^{3}= 999$

$\implies x^{3}= {\frac{999}{37}}$

$\implies x^{3}= 27$

$\implies x={\sqrt[3]{27}}$

$\implies x= 3$

$\huge\bold{\mathbb{HENCE}}$

$x = 3$

• $3x = (3 \times 3) = 9$

• $4x = (4 \times 3) = 12$

$\huge\bold{\mathbb{THEREFORE}}$

The numbers are $9$ and $12$ respectively.

$\huge\bold{\mathbb{NOT\:SURE\:??}}$

$\huge\bold{\mathbb{VERIFICATION}}$

$(4x)^{3}-(3x)^{3} = 999$

Putting the values of $3x$ and $4x$.

$\implies 12^{3}-9^{3} = 999$

$\implies 1728-729 = 999$

$\implies 999 = 999$

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

Hence, verified ✓ .

$\huge\bold{\mathbb{DONE}}$