Question

Q.6 The present age of Ridhi and Sidhi are in ratio 5:7. If 5 is added to the age of both them
ratio becomes 11:15. Find their present ages.​

Answer 1

Required Answer:-

Given:

• The present age of Ridhi and Sidhi are in the ratio 5 : 7.
• If 5 is added to the age of both of them, the ratio becomes 11 : 15

To find:

• The present ages of Ridhi and Sidhi.

Solution:

Let the ages of Ridhi and Sidhi be 5x and 7x

After adding 5 to their ages,

➡ Ridhi's Age = 5x + 5

➡ Sidhi's Age = 7x + 5

According to the given condition,

➡ (5x + 5)/(7x + 5) = 11/15

On cross multiplying, we get,

➡ 15(5x + 5) = 11(7x + 5)

➡ 75x + 75 = 77x + 55

➡ 77x - 75x = 75 - 55

➡ 2x = 20

➡ x = 10.

Hence,

• Present age of Ridhi will be = 5x = 50 years.
• Present age of Sidhi will be = 7x = 70 years.

Answer:

• The present age of Ridhi is 50 years.
• The present age of Sidhi is 70 year.

Verification:

Let's verify our result.

Ratio of their ages is,

50 :.70

= 5 : 7 which is correct ✔

Adding 5 to both of their ages, we get ages 55 and 75.

Ratio will be,

= 55 : 75

= 11 : 15 which is also correct ✔

Hence, our answers are correct (Verified ✔)

Answer 2

$\huge{ \green{ \underline{ \mathfrak{Given:}}}}$

• Ratio of present ages of ridhi and sidhi = 5:7
• Ratio (After adding 5) = 11:15

$\huge{ \green{ \underline{ \mathfrak{To \: Find: }}}}$

• Present ages of ridhi and sidhi

$\huge{ \green{ \underline{ \mathfrak{Solution: }}}}$

Put x in the ratio ,

• Present age of Ridhi = 5x
• Present age of Sidhi = 7x
• Age of Ridhi (After adding 5) = 5x + 5
• Age of Sidhi (After adding 5) = 7x + 5

According to question,

$\large{ \sf : \implies \: \: \: \: \: \: \: \: \frac{5x + 5}{7x + 5} = \frac{11}{15}}$

After cross multiplication,

$\large{ \sf : \implies \: \: \: \: \: \: \: \: 15(5x + 5) = 11(7x + 5)}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: 75x + 75 = 77x + 55}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: 75x - 77x = 55 - 75}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: - 2x = - 20}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: x = \frac{ - 20}{ - 2} }$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: x = 10}$

Now:

• Present age of Ridhi = 5x = 50 years
• Present age of Sidhi = 7x = 70 years

$\huge{ \green{ \underline{ \mathfrak{Hence:}}}}$

• The ages of ridhi and sidhi are 50 years and 70 years