Question

if the numbers are in ratio 5:8 if 9 is added to each they are in the ratiol 8:11 find the number
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Answer 1

Given :

• Ratio of two numbers = 5:8
• If 9 is added to each they are in the ratiol 8:11.

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To find :

• Numbers?

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Solution :

☯ Let the numbers be 5x and 8x.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• If 9 is added to each they are in the ratiol 8:11.

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$:\implies\sf \dfrac{5x + 9}{8x + 9} = \dfrac{8}{11}$

$:\implies\sf 11(5x + 9) = 8(8x + 9)$

$:\implies\sf 55x + 99 = 64x + 72$

$:\implies\sf 55x - 64x = 72 - 99$

$:\implies\sf 9x = 27$

$:\implies\sf x = \cancel{ \dfrac{27}{9}}$

$:\implies{\boxed{\sf{\pink{x = 3}}}}\;\bigstar$

Therefore,

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• First number, 5x = 5 × 3 = 15

• Second number, 8x = 8 × 3 = 24

Answer 2

Question :-

Two numbers are in ratio 5:8 if 9 is added to each they are in the ratiol 8:11 find the number

Answer :-

$\large\sf\underline\red{Given:}$

• Two numbers are in the ratio 5:8

• 9 added to these numbers then the ratio 8:11

$\large\sf\underline\red{To\:find:}$

Find the numbers

$\large\sf\underline\red{Solution:}$

Let,

The first number = 5x

and the second number = 8x

ATQ,

$\sf{\implies \dfrac{5x+9}{8x+9}=\dfrac{8}{11}}$

$\sf{\implies 8(8x+9)=11(5x+9)}$

$\sf{\implies 64x+72=55x+99}$

$\sf{\implies 64x–55x=99–72}$

$\sf{\implies 9x=27}$

$\boxed{\bf{\blue{x=3}}}$

So,

the 1st number is 5x = 5×3 = 15

and the 2nd number is 8x = 8×3 = 24

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