Question

Two number are in the ratio 5:8 if 8 subtracted from each other number the ratio becomes 4:5. Find the numbers

Answer 1

Let the numbers in the ratio 5 : 8 be 5x and 8x

If 8 is subtracted from 5x and 8x, the number becomes 5x - 8 and 8x - 8

if 8 subtracted from each other number the ratio becomes 4 : 5 = 4x and 5x



According to the question,

5x - 8 + 8x - 8 = 4x + 5x

13x - 16 = 9x

13x - 9x = 16

4x = 16

x = $\dfrac{16}{4}$

x = 4




1st number => 5x

=> 5 × 4

=> 20


2nd number => 8x

=> 8 × 4

=> 32




$\therefore{}$ The numbers are 20 and 32 respectively.

Answer 2

$dear \: friend \:$


here is your answer OK ☺☺☺☺☺☺


Let 1st number (numerator) be x ☺☺☺☺

let 2nd number (denominator) be y ☺☺☺☺

they are in ratio so theri ratio = x / y ☺☺☺

as per sum

1 condition = x / y = 5 / 6

6x = 5y

6x - 5y = 0 ----- 1

2 condition = x-8 / y-8 = 4 / 5

5x - 4y = -32 + 40

5x - 4y = 8 ------- 2

By substitution method

x = 5y / 6 (from 1)

putting value of x in equation 2

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

25y - 24y / 6 = 8

25y - 24y = 8 X 6

y = 48

putting value of y in equation 1 ☺☺☺☺

6x - 5(48) = 0

6x = 240

x = 240 / 6

x = 40

Value of x = 40

Value of y = 48