Question

the between two numbers ratio is5:8 when add 9 each number ratio is 8:11 so find which of the two numbers?

Answer 1

the two numbers are 15 and 24.

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Answer 2

LET THE NUMBERS BE x & y respectively.

by the first given condition

$\frac{x}{y } = \frac{5}{8}$

$8x = 5y$

$8x - 5y = 0.................(1)$
by the second given condition

$\frac{x + 9}{y + 9} = \frac{8}{11}$

$11(x + 9) = 8(y + 9)$

$11x + 99 = 8y + 72$

$11x - 8y = 72 - 99$
11x-8y=-27.............(2)

[multiplying eq no. (1 ) by 8 & eq no. (2) by 5]

64x-40y=0.....................(3)
55x-40y=-135.........................(4)

[subtracting eq no. (4) from eq no.(3) ]
9x=135
x=135/9
x=15

substituting x=15 in eq no. (1) we get

8x-5y=0
8(15)-5y=0
120=5y
y=24

THEREFORE,
THE TWO NUMBERS ARE 15 and 24.

HOPE THIS HELPS!!!