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

Given: 

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

To do: 

We have to find the numbers.

Solution: 

Two numbers are in the ratio $ 5 : 6$.

Let the numbers be $5x$ and $6x$.

If 8 is subtracted from each number then it becomes $4 : 5$.

Therefore,

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

$\frac{5x - 8}{6x - 8} = \frac{ 4}{ 5}$

On cross multiplication, we get,

$(5 x - 8)\times 5  =  4 \times (6 x -8)$

Multiplying the numbers inside the brackets,

$25 x  - 40  =  24 x - 32$

$25 x - 24 x  =  -32 + 40$     (Keep variables on one side and numbers on the other side)

$x = 8$

This implies,

$5x=5(8)=40$ and

$6x=6(8)=48$

Therefore the numbers are 40 and 48 respectively.

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Updated on: 10-Oct-2022

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