Question

Two number are in the ratio 4:5. If differences between their cubes is 61, find the numbers.

Answer 1

Answer:

4 and 5

Given:

Two numbers in ratio 4:5.Differences between their cubes is 61.

To find:

The numbers

Solution:-

Let the numbers be 4x and 5x

Then

According to the question

${(4x)}^{3} - {(5x)}^{3} = 61$

${64x}^{3} - {125x}^{3} = 61$

$61{x}^{3} = 61$

${x}^{3} = \frac{61}{61}$

${x}^{3} = 1$

$x = \sqrt[3]{1}$

$x = 1$

4x=4×1

=4

5x=5×1

=5

___________________

Therefore;

The numbers are 4 and 5

Answer 2

Answer:

Two number are in the ratio 4:5 .If differences between their cubes is 61.

Find the numbers .

Suppose the numbers = 4x or 5x

= (4x)^3 - (5x)^3 = 61

= 64x^3 - 125x^3 = 61

= 61x^3 = 61

x^3 = 61

61

x^3 = 1

x = 3cube 1

x =1

4x =4 × 1

= 4

5x =5 × 1

=5

The numbers are 4 or 5 .