Two numbers are in the ratio 8: 9 . If 6 is subtracted from each, the ratio becomes 5: 6
find the numbers.

Given: Two numbers are in the ratio 8: 9. If 6 is subtracted from each, the ratio becomes 5: 6 

To do: Find the numbers

Solution:
Two numbers are in the ratio $ 8 : 9$

so, the numbers are  $8 x$  and  $9 x$

If 6 is subtracted from each number then it becomes 5 : 6

$\frac{8 x - 6}{9 x - 6} = \frac{ 5}{ 6}$

Cross multiply

$(8 x - 6)\times 6  =  5 \times (9 x -6)$

Multiply the numbers inside the brackets,

$48 x  - 36  =  45 x - 30$

$48 x - 45 x  =  -30 + 36$     (keep variables on one side and numbers on the other side)

$3 x   =  6$

$x   =  \frac{6}{ 3}$

$x   =  2$

Therefore the numbers are,

$8 (2) :  9 (2)$

$16 : 18$

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Updated on: 10-Oct-2022

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