Question

Two numbers are in the ratio 3:4. If the difference of their cubes is 999
then difference of the numbers is
(B) 4
(C) 3
(A) 5
(E) None of these
(D) 2.
The marks obtained by three students in a fost are in the ratio of 2:3;4.​

Answer 1

Step-by-step explanation:

Given:

• Ratio of the numbers
• Difference of their cubes

To Find:

• The difference of the two numbers

Solution;

Let the two numbers be 3x and 4x respectively.

Cube of 1st number

$\tt \longrightarrow \: ( {3x})^{3 } = 27 {x}^{3}$

Cube of 2nd number

$\tt \longrightarrow(4x) ^{3} = 64 {x}^{3}$

Here 64x^3 is greater so we subtract 27x^3 from it.

ACQ,

$\tt \longrightarrow\therefore \: 64 {x}^{3} - 27 {x}^{3} = 999 \\ \tt \longrightarrow37 {x}^{3} = 999 \\ \tt \longrightarrow {x}^{3} = \frac{ \cancel{999}}{ \cancel{37}} = 27 \\ \tt \longrightarrow \: x = \sqrt[3]{27} = 3$

So,

The numbers are 3×3 and 4×3

=9 and 12

Difference of the numbers=

$\tt \longrightarrow \: 12 - 9 = \red3$