Question

numbers are in the ratio of 5.6
if 8 is subtracted
from
each of the number the ratio
becomes 4:5, Find the numbers.
​

Answer 1

Answer:

If 8 is subtracted from each of the numbers , the ratio becomes 4:5 find the numbers. If 8 is subtracted from each of the numbers then the ratio is 4:5. Therefore the numbers are 40 and 48.

Step-by-step explanation:

Answer 2

Given :-

Two numbers are in the ratio 5 : 6

When 8 is subtracted from each of the numbers, the ratio becomes 4 : 5

To Find :-

The first number.

The second number.

Analysis :-

Consider both the numbers as variables.

Make equation in both the cases and substitute the values accordingly.

Find the value of both the numbers.

Solution :-

Let the two numbers be 'x' and 'y' respectively.

Given that,

Two numbers are in the ratio 5 : 6

$\sf \dfrac{x}{y} =\dfrac{5}{6}$

$\sf x \times 6 = y \times 5$

$\sf 6x - 5y = 0 \quad ....(1)$

When 8 is subtracted from each of the numbers, the ratio becomes 4 : 5

Then,

$\sf \dfrac{x-8}{y-8} =\dfrac{4}{5}$

$\sf 5x - 40 = 4y -32$

According to the question,

$\sf 5x - 4y = 8 \quad ...(2)$

Now,

$\sf 5 x - 4 y - 8 = 0 \times6$

$\sf 30 x - 24 y - 48 = 0 \quad ....(3)$

By subtracting,

$\sf y - 48 = 0$

$\sf y = 48$

Substituting the value of y,

$\sf \dfrac{x}{y} =\dfrac{5}{6}$

$\sf \dfrac{x}{48} =\dfrac{5}{6}$

Finding the value of x,

$\sf x=5 \times \dfrac{48}{6}$

$\sf x=5 \times 8$

$\sf x=40$

Therefore, the two numbers are 48 and 40 respectively.