Question

two no. are in the ratio 7:11 if 7added to each of number the ratio becomes 2:3 find the number​

Answer 1

Answer :-

• The numbers are 49 and 77.

Given :-

• Two numbers are in the ratio 7 : 11.
• If 7 is added to each of the numbers, the ratio becomes 2 : 3.

To find :-

• The numbers.

Step-by-step explanation :-

• Two numbers are in the ratio 7 : 11.

• So, let the numbers be 7x and 11x respectively.

• It has been given that, if 7 is added to each of the numbers, the ratio becomes 2 : 3.

Adding 7 to each of the numbers,

$\bf7x = 7x + 7$

$\bf11x = 11x + 7$

So, the ratio of 7x + 7 and 11x + 7 is 2 : 3.

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$\longmapsto \sf\dfrac{7x + 7}{11x + 7} = \dfrac{2}{3}$

By cross multiplication,

$\longmapsto\sf3 \: (7x + 7) = 2 \: (11x + 7)$

Removing the brackets,

$\longmapsto\sf21x + 21 = 22x + 14$

Putting the constant and variable terms on different sides by the method of transposition,

$\longmapsto\sf21x - 22x = 14 - 21$

On simplifying,

$\longmapsto\sf \cancel{-} x= \cancel{-} 7$

Cutting off the negative sign,

$\longmapsto \overline{\boxed{\sf x = 7}}$

• The value of x is 7.

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Hence, the numbers are as follows :-

$\rm7x = 7 \times 7 = 49$

$\rm11x = 11 \times 7 = 77$

Answer 2

Given :

• Two numbers are in ratio 7:11.
• If 7 is added to them then the ratio becomes 2:3.

To Find :

• The Numbers

Solution :

⟼ Let first number be 7k

⟼ Let second number be 11k

After adding 7 :

⟼ First number will become 7k + 7

⟼ Second number will become 11k + 7

⠀

According to the Question :

⟹ 7k + 7 / 11k + 7 = 2/3

⟹ 3 (7k + 7) = 2 (11k + 7)

⟹ 21k + 21 = 22k + 14

⟹ 21k - 22k = 14 - 21

⟹ k = 7

Therefore :

• First Number = 7k = 7 × 7 = 49
• Second Number = 11k = 11 × 7 = 77

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