Question

Two numbers are in the ratio 5: 11. If 5 is added to each of the numbers, the ratio

becomes 5: 9. Find the numbers.​

Answer 1

Answer:

Let the numbers be 5x and 11 x

By adding 5 to each of the number

Fraction becomes ⬇️⬇️⬇️⬇️⬇️

$\frac{5x + 5}{11x + 5}$

▪️◾◼️ According to question ▪️◾◼️

$\frac{5x + 5}{11x + 5} = \frac{5}{9} \\ \\ = 9(5x + 5) =5(11x + 5) \\ 45x + 45 = 55x + 25 \\ 55x - 45x = 45 - 25 \\ 10x = 20 \\ x = 2$

Therefore The numbers are

⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️

$5x = 5 \times 2 = 10 \\ 11x = 11 \times 2 = 22$

Answer 2

Answer:

The two numbers are 10 and 22.

Step-by-step explanation:

Given :-

• Two numbers are in the ratio 5:11.
• If 5 is added to each of the numbers, the ratio becomes 5: 9.

To find :-

• The two numbers.

Solution :-

Consider,

• 1st number = 5x
• 2nd number = 11x

★ If 5 is added to each of the numbers, the ratio becomes 5:9.

• 1st number = (5x+5)
• 2nd number = (11x+5)

According to the question,

$\to\sf{(5x+5):(11x+5)=5:9}$

$\to\sf{\dfrac{5x+5}{11x+5}=\dfrac{5}{9}}$

$\to\sf{55x+25=45x+45}$

$\to\sf{55x-45x=45-25}$

$\to\sf{10x=20}$

$\to\sf{x=2}$

Therefore,

★ 1st number = 5×2 = 10

★ 2nd number = 11×2 = 22

___________________

Verification :-

• 1st number = 10
• 2nd number = 22

Ratio of two numbers = 5:11

→ 10:22 = 5:11

→ 5:11 = 5:11

★ If 5 is added to each of the numbers, the ratio becomes 5:9.

(1st no. + 5):(2nd no. +5) = 5:9

→ (10+5):(22+5)= 5:9

→ 15:27=5:9

→ 5:9 = 5:9

Hence Verified !