Question

(1.) Two numbers are in the ratio 5:6. If 5 is added to both the numbers then the ratio of the numbers becomes 6:7. Find the numbers.​

Answer 1

Given:

Two numbers are in the ratio of 5:6

Now,

Let one number be 5x

And another number be 6x

Now

According to the question,

If 5 is added to both the numbers then the ratio of the numbers becomes 6:7

The required, equation, will become

⇒ $\frac{5x+5}{6x+5} =\frac{6}{7}$

⇒ 6(6x+5) = 7(5x+5)

[By doing cross multiplication]

⇒ 6(6x) + 6(5) = 7(5x) + 7(5)

⇒ 36x + 30 = 35x + 35

⇒ 36x - 35x = 35 - 30

[Taking 35x to LHS, and taking 30 to RHS]

⇒ 1x = 5

∴ x = 5

Therefore,

The value of x is 5

So, the numbers are

= 5x = 5 × 5 = 25

And

= 6x = 6 × 5 = 30

Hence,

The number are 25 and 30.

- - -

Verification:

25 ÷ 30

[both are divisible by 5]

[25 ÷ 5 = 5 and 30 ÷ 5 = 6]

So,

25 ÷ 30 = 6:7