Question

Two numbers are in the ratio 7:11. If 7 is added to each of the number, the ratio becomes 2:3. Find the numbers. PLEASE GIVE CLEAR EXPLAINATION.
(ANSWER - 49 AND 77)

Answer 1

Answer:

The Numbers are 49 and 77.

Step-by-step explanation:

Given :

Ratio of the numbers = 7 : 11

Ratio of the numbers when 7 is added to each number = 2 : 3

To find :

The numbers

Solution :

Let the numbers be -

• One as 7x
• Second as 11x

★ $\boxed{\sf{\frac{7x + 7}{11x + 7} = \frac{2}{3}}}$

$\sf{\implies} \: \dfrac{7x + 7}{11x + 7} = \dfrac{2}{3} \\ \\ \sf{\implies} \: 3(7x + 7) = 2(11x + 7) \\ \\ \sf{\implies} \: 21x + 21 = 22x + 14 \\ \\ \sf{\implies} \: 22x - 21x = 21 - 14 \\ \\ \sf{\implies} \: x = 7$

$\rule{300}{1.5}$

★ Value of 7x

$\sf{\implies} \: 7(7) \\ \\ \sf{\implies} \: 49$

One Number = 49

$\rule{300}{1.5}$

★ Value of 11x

$\sf{\implies} \: 11(7) \\ \\ \sf{\implies} \: 77$

Second Number = 77

$\therefore$ The Numbers are 49 and 77.

Answer 2

Answer:

The numbers are :

49 and 77

Step-by-step explanation:

Given :

Two numbers are in the ratio 7 : 11.

If we add 7 to each of the number, the ratio becomes 2 : 3.

To Find :

The numbers.

Solution :

Consider the :

The ratio as - 'y'

So,

The numbers are 7y and 11y.

According to the statement :

If we add 7 to each of the number, the ratio becomes 2 : 3.

______________{ Given! }

So,

$\sf\\ \\\implies \dfrac{7y+7}{11y+7}\\ \\ \\ \implies \dfrac{2}{3}$

Now,

$\sf\\ \\\implies 3(7y+7)=2(11y+7)\\ \\ \\\implies 21y+21=22y+14\\ \\ \\\implies 7=y\\ \\ \\\implies y= 7$

Therefore,

$\sf \implies 7y = 7 \times 7 =49$

$\sf \implies 11y = 11\times7 = 77$

Hence,

The numbers are 49 and 77.