Question

Two numbers are in the ratio of 4 : 5. if 4 added to each number, then their ratio is 5 : 6, find the numbers.

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Answer 1

GIVEN :-

• Two numbers are in the ratio of 4 : 5.
• 4 added to each number.

TO FIND :-

• The numbers.

SOLUTION :-

Let the ratio constant be "x".

★ After adding 4 to each number,

• Number are 4x + 4 and 5x + 4

$\\ : \implies \displaystyle \sf \: \frac{4x + 4}{5x + 4} = \frac{5}{6}$

$: \implies \displaystyle \sf \: 5(5x + 4) = 6(4x + 4)$

$: \implies \displaystyle \sf \: 25x + 20 = 24x + 24$

$: \implies \displaystyle \sf \: 25x - 24x = 24 - 20$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x =4 }}$

Now , by substituting the value of x , Lets find the required numbers.

⇢ 1st number = 4x

⇢ 1st number = 4 × 4

⇢ 1st number = 16

Similarly,

⇢ 2nd number = 5x

⇢ 2nd number = 5 × 4

⇢ 2nd number = 20

Hence the required numbers are 16 and 20.

Answer 2

Question:-

Two numbers are in the ratio of 4 : 5. if 4 added to each number, then their ratio is 5 : 6, find the numbers.

Answer:-

• The required numbers are 16 and 20.

To find:-

• The number

Solution:

Put x in the ratio.

• After adding 4

Let the number be :-

• 4x + 4
• 5x + 4

$\large{ : \implies \: \frac{4x + 4}{5x + 4} = \frac{5}{6} }$

After cross multiplication

$\large{ : \implies \: 6(4x + 4) = 5(5x + 4)}$

$\large{ : \implies \: 24x + 24 \: = 25x + 20}$

$\large{ : \implies \: 24x - 25x = 20 - 24}$

$\large{ : \implies \: \cancel - x = \cancel - 4}$

$\large{ : \implies \: x = 4}$

• The value of x is 4

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NUMBERS ARE :-

• First number = 4x= 4×4 = 16
• Second number = 5x = 5×4 = 20

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The required numbers are 16 and 20.