Question

Two numbers are in the ratio 3:5. When 8 is added to each, the ratio changes
to 5: 7. Identify the two numbers​

Answer 1

Answer:

two numbers are 12 and 20

Step-by-step explanation:

let two numbers be 3x and 5x

3x+8=5x and 5x+8=7x

8=5x-3x

8=2x

x=4

3x=3x4=12

5x=5x4=20

Answer 2

To Find :-

• The two numbers

Solution:

Given that,

• The two numbers are in the ratio = 3:5

$\textsf{ \textbf{\dag \: {\underline{Assumption}}}}$

Let us assume the two numbers as 3x and 5x.

Also given,

• When, 8 is added to each, the ratio changes to 5:7

Therefore,

$\underline{\boxed{\tt{\dfrac{3x + 8}{5x + 8} = \dfrac{5}{7}}}}$

⠀⠀⠀⠀⠀ ⠀⠀_______________________

According the Question,

• The two numbers are :-

$\tt{ \implies \: \dfrac{3x + 8}{5x + 8} = \dfrac{5}{7}}$

$\tt{ \implies \: 7(3x + 8) = 5(5x + 8)}$

$\tt{ \implies \: 21x + 56 = 5(5x + 8)}$

$\tt{ \implies \: 21x + 56 = 25x + 40}$

$\tt{ \implies \: 21x - 25x + 56 = 40}$

$\tt{ \implies \: 21x - 25x = 40 - 56}$

$\tt{ \implies \: - 4x = - 16}$

$\tt{ \implies \: 4x = 16}$

$\tt{ \implies \: \dfrac{16}{4}}$

$\tt{ \implies \: \dfrac{ \cancel{16}}{ \cancel{4}}}$

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

The value of x is 4. The numbers are :-

• 3x = 3*4 = 12
• 5x = 5*4 = 20

Hence, The numbers are 12 and 20.

Required Answer:-

• The two numbers = 12 and 20.