Question

two numbers are in the ratio 5:6,if 8 is subtracted each,the ratio becomes 4:5.find the numbers?​

Answer 1

Given question:-

• Two numbers are in the ratio 5:6.
• If 8 is subtracted each.
• The ratio becomes 4:5.

To Find:-

We needs to find the two numbers.

Solution:-

Let the common factor be x

1st number = 5x

2nd number = 6x

If 8 is subtracted from each of the number,

1st number = 5x - 8

2nd number = 6x - 8

The ratio becomes 4:5

Then, the equation will be

$\frac{5x - 8}{6x - 8} = \frac{4}{5}$

25x - 40 = 24x - 32

25x - 24x = - 32 + 40

x = 8

So,

1st number = 5x = 5(8) = 40

2nd number = 6x = 6(8) = 48

Thus,

Two numbers are 40 and 48

Don't confuse. I will verify it.

Verification:-

• In question the ratio is 5:6. we will check that,

$\frac{40}{48} = \frac{5}{6}$

= 5:6

• If 8 is subtracted from each, it's ratio becomes 4:5

We will check that,

$\frac{40 - 8}{48 - 8} = \frac{32}{40}$

$= \frac{32}{40}$

$= \frac{8}{10}$

$= \frac{4}{5}$

Hence, we verified it.

So, our answer is correct.