Question

Two numbers are in ratio of 5:6 and 8 is subtracted from each number then the ratio is 4:5 find the numbers

Answer 1

Let the number be ‘x’.

The ratio of two numbers are 5:6

i,e 5x : 6x

When subtract with 8 then

(5x-8)/(6x-8)

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

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

25x-40=24x-32

25x-24x=40-32

x=8

The number is 8.

Answer 2

Given :-

• Ratio of the two numbers = 5 : 6.
• New ratio ( after subtracting 8 from both numbers) = 4 : 5.

To Find :-

• The two numbers.

Solution :-

Let the two numbers be x and y.

According to the question,

⇒ x/y = 5/6

⇒ x = 5y/6........( 1 )

Also,

⇒ x - 8/y - 8 = 4/5

⇒ 5(x - 8) = 4(y - 8)

⇒ 5x - 40 = 4y - 32

⇒ 5x - 4y = 40 - 32

⇒5x - 4y = 8.......( 2 )

Substituting ( 1 ) in ( 2 ) gives,

⇒ 5 × 5y/6 - 4y = 8

⇒ 25y/6 - 4y = 8

⇒ 25y - 24y/6 = 8

⇒ y/6 = 8

⇒ y = 8 × 6 = 48

Substituting the value of y in ( 1 ) gives,

⇒ x = 5 × 48/6

⇒ x = 240/6

⇒ x = 40

∴ Numbers are 40 and 48.