Question

Two numbers are in the ratio 5 : 6 , if 8 is subtracted from each of the number

the ratio is 4:5 . Find the numbers.​

Answer 1

Answer:

let the number be 5x and 6x

given 5x -8 / 6x - 8 = 4/ 5

= 25x - 40 = 24x - 32

= x = 8

so numbers are 5x = 5×8 =40

and 6x = 6×8 =48

Answer 2

Answer :-

• The two numbers are 40 and 48.

Given :-

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

To find :-

• The numbers.

Step-by-step explanation :-

• Two numbers are in the ratio 5 : 6. So let them be 5x and 6x respectively.

Subtracting 8 from both of them,

• 5x will be 5x - 8.
• 6x will be 6x - 8.

It has been given that :-

• If 8 is subtracted from each of the numbers, the ratio is 4 : 5.

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Hence,

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

By cross multiplication,

$\sf5 \: (5x - 8) = 4 \: (6x - 8)$

Removing the brackets,

$\sf25x - 40 = 24x - 32$

Putting the constant and variable terms on different sides by the method of transposition.

$\sf25x - 24x = - 32 + 40$

On simplifying,

$\overline{\boxed{\sf x = 8}}$

• The value of x is 8.

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So, the numbers are :-

$\bf 5x = 5 \times 8 = 40.$

$\bf 6x = 6 \times 8 = 48.$