Question

Two numbers are in the ratio 5 ratio 6 if 8 is subtracted from each number the ratio becomes 4 ratio 5 the smaller number is

Answer 1

Given :

Two numbers are in ratio 5:6

So,

let one number be 5x and another be 6x

Now,

According to the question,

When 8 is subtracted from each number the ratio becomes 4:5

 

To be found :-

The smaller number

 

So,

here is the equation

 

⇒ $\bf \frac{5x-8}{6x-8}=\frac{4}{5}$

⇒ $\bf 5(5x-8)=4(6x-8)$     [by cross multiplication]

⇒ $\bf 25x - 40 = 24x-32$

⇒ $\bf 25x - 24x = 40 -32$  [taking 24x to LHS and -40 to RHS]

⇒ x = 8

∴ the value of x = 8

Now,

One number = 5x = 5 × 8 = 40

another number = 6x = 6 × 8 = 48

Hence

The smallest number is 40

Answer 2

$\sf\underline{Step-by-step \: explanation}$

Let the common multiple be x

According to the question,

$\tt\dfrac{5x \: - \: 8}{6x \: - \: 8}$ = $\tt\dfrac{4}{5}$

[m : n = m/n]

Doing cross multiplication,

5(5x - 8) = 4(6x - 8)

25x - 40 = 24x - 32

24x - 25x = -40 + 32

-x = -8

x = 8 [Minuses cancel each other]

So, the first number is,

5x = 5 × 8 = 40

Second number,

6x = 6 × 8 = 48

As 40 < 48, So 40 is the smaller number.