Question

The two number are in the ratio 5 ratio 8 if 9 be added to each other and are in the ratio of 8 ratio 11 find the number

Answer 1

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The two numbers are in ratio 5 : 8. So, let's consider the numbers be 5x and 8x.

Now 9 is added to the numbers. Then the numbers would be 5x + 9 and 8x + 9. According to question,

⇛ $\rm{ \dfrac{5x + 9}{8x + 9} = \dfrac{8}{11} }$

The ratio becomes 8 : 11. Now solving the above equation to find the numbers,

⇛ $\rm{11(5x + 9) = 8(8x + 9)}$

Expanding the parentheses,

⇛ $\rm{55x + 99 = 64x + 72}$

Isolating x in any one of the equation,

⇛ $\rm{64x - 55x = 99 - 72}$

This would be equals to,

⇛ $\rm{9x = 27}$

Then, x will be equals to 3

$\therefore$ The required numbers are:

• 5x = 5(3) = 15
• 8x = 8(3) = 24

And we are done!

Answer 2

Answer:

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The two numbers are in ratio 5 : 8. So, let's consider the numbers be 5x and 8x.

Now 9 is added to the numbers. Then the numbers would be 5x + 9 and 8x + 9. According to question,

⇛ $\rm{ \dfrac{5x + 9}{8x + 9} = \dfrac{8}{11}}$

The ratio becomes 8 : 11. Now solving the above equation to find the numbers,

⇛ 11(5x+9)=8(8x+9)

Expanding the parentheses,

⇛ 55x+99=64x+72

Isolating x in any one of the equation,

⇛ 64x−55x=99−72

This would be equals to,

⇛9x=27

Then, x will be equals to 3

∴ The required numbers are:

5x = 5(3) = 15

8x = 8(3) = 24