Question

Two numbers are in ratio 7:11 if 7 is added to each , ratio become 2:3 find the number​

Answer 1

Answer:

• 49 and 77

Given:-

• Two numbers are in ratio 7:11
• if 7 is added to each , ratio become 2:3

To Find:-

• The numbers

Step-by-step explanation:

As given, the two numbers are in ratio 7 : 11

Let the common factor of ratio be x, where x ≠0

Then, two numbers are 7x and 11x

Now, 7 is added to each and ratio becomes 2 : 3

According to the question,

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

$\implies \sf \: 3(7x + 7) = 2(11x + 7)$

$\implies \sf \: 21x + 21 = 22x + 14$

$\implies \sf \: 22x - 21x = 21 - 14$

$\boxed{ \red{ \implies \sf{x = 7}}}$

Therefore, two numbers are (7×7)=49 and (11×7)=77.

Answer 2

Answer :-

• The numbers are 49 and 77.

Given :-

• Two numbers are in ratio 7 : 11 if 7 is added to each, ratio become 2 : 3.

To Find :-

• The numbers.

Solution :-

Put x in the ratio

Numbers are

• 7x
• 11x

7 added to each

• 7x + 7
• 11x + 7

Here

• When 7 is added to each, the ratio becomes 2 : 3.

According to question :-

⇒ 7x + 7/11x + 7 = 2/3

⇒ 3 (7x + 7) = 2 (11x + 7)

⇒ 21x + 21 = 22x + 14

⇒ 21 - 14 = 22x - 21x

⇒ x = 7

Put the value of x in the ratio

Now

• 7x = 7 × 7 = 49
• 11x = 11 × 7 = 77

Hence, the numbers are 49 and 77.