Question

Two numbers are in the ratio 5 : 9. on subtracting 3 form each, the ratio becomes 1 : 2. Find the numbers​

Answer 1

Answer:

The numbers are 15 & 27

Step-by-step explanation:

Given that,

Two numbers are in ratio 5 : 9 on subtracting 3 from each the ratio becomes 1 : 2

Here, the ratio 5 : 9 turns 1 : 2 after subtraction of 3 in each number.

Step 1 :

Considering the numbers :

→ "5x"

→ "9x"

Step 2 :

Subtracting 3 from both the numbers :

→ "5x - 3"

→ "9x - 3"

Step 3 :

The ratio now is 1 : 2

So,

→ (5x - 3)/(9x - 3) = 1/2

Step 4 :

Solving for "x" :

→ (5x - 3)/(9x - 3) = 1/2

→ 2(5x - 3) = 1(9x - 3)

→ 10x - 6 = 9x - 3

→ 10x - 9x = 6 - 3

→ x = 3

∴ The value of "x" is 3

Hence,

The numbers are :

→ 5x = 5(3) = 15

→ 9x = 9(3) = 27

____________________

★ Verification :

• If we again subtract the numbers by 3 we must get the ratio 1 : 2

Again,

Subtracting 3 from both the numbers :

→ 15 - 3 = 12

→ 27 - 3 = 24

• We got the numbers as 12 & 24

Forming in ratio :

→ 12 : 24

→ 12/24 [dividing by 12]

→ 1/2

→ 1 : 2

∵ we got the ratio again 1 : 2

Hence, verified ✔

_____________________

Answer 2

Answer :-

• The Numbers are 15 and 27.

Explanation :-

Given :

• Two numbers are in the ratio 5 : 9.

• On subtracting 3 from each number, the ratio becomes 1 : 2.

To Find :

• Both the numbers.

Solution :

Let the numbers be 5x and 9x.

According to the Question,

⇒ (5x - 3)/(9x - 3) = 1/2.

⇒ 2(5x - 3) = 9x - 3.

⇒ 10x - 6 = 9x - 3.

⇒ 10x - 9x = 6 - 3.

⇒ x = 3.

Therefore, The numbers are :

• 5x = 15.
• 9x = 27.