Question

The ages of Sona and Mona are in the ratio 5:3. Five years later, the ratio of their ages will be 10:7. Find their ages after 10 years.

Answer 1

Step-by-step explanation:

It is given that the ratios of Sona and Mona are 5:3.

Let the ratio constant of the ages be x.

So, the present ages will be :-

• Sona - 5x
• Mona - 3x

After 5 years,

The ages will get added up to 5, because we advanced 5 years aahead.

So, the ages will be :-

• Sona - 5x+5
• Mona - 3x+5

Now, the fractions will result in :-

$\sf{\dfrac{5x+5}{3x+5} = \dfrac{10}{7}}$

Now, cross multiply the equations :-

$\sf{7(5x + 5) = 10(3x + 5)}$

$\sf{35x + 35 = 30x + 50}$

$\sf{35x + 35 = 30x + 50}$

$\sf{5x = 15}$

$\sf{x = 3}$

So, we got the ratio constant as 3.

Now, present ages of Sona and Mona are :-

• 5×3 = 15 years
• 3×3 = 9 years.

No, we are asked to find their ages after 10 years.

So, 15+10 = 25 years and 9+10 = 19 years respectively.

The ages of Sona and Mona will be 25 years and 19 years respectively.

Answer 2

Question:

• The ages of Sona and Mona are in the ratio 5:3. Five years later, the ratio of their ages will be 10:7. Find their ages after 10 years.

Answer:

• Ages of Sona and Mona after 10 years are 25 years and 19 years.

Explanation:

Given that:

• Ratio of ages of Sona and Mona = 5:3.
• Five years later, ratio of their ages will be = 10:7.

To Find:

• Their ages after 10 years?

Solution:

• Let ages of Sona and Mona be 5n years and 3n years.
• So, five years later, their ages will be (5n + 5) years and (3n + 5) years.

According to the question,

• Five years later, the ratio of their ages will be 10:7.

Therefore,

➻ $\sf \dfrac{5n + 5}{3n + 5} = \dfrac{10}{7}$

By doing cross multiplication we get,

➻ $\sf 7(5n + 5) = 10(3n + 5)$

➻ $\sf 35n + 35 = 30n + 50$

➻ $\sf 35n - 30n = 50 - 35$

➻ $\sf 5n = 15$

➻ $\sf n = {\cancel{\dfrac{15}{5}}}$

➻ $\bf \red{n = 3}$

Hence,

⇒ Present age of Sona = 5n

⇒ Present age of Sona = 5 × 3

➠ Present age of Sona = 15 years

↦ Age of Sona after 10 years = (15 + 10) years

➦ Age of Sona after 10 years = 25 years

Also,

⇒ Present age of Mona = 3n

⇒ Present age of Mona = 3 × 3

➠ Present age of Mona = 9 years

↦ Age of Mona after 10 years = (9 + 10) years

➦ Age of Mona after 10 years = 19 years

∴ Their ages after 10 years are 23 years and 19 years.

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