Question

The ages of Sita and Gita are in the ratio 3:5. After 5 years, their ratio will become 2:3. Find their ages.

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Answer 1

Sita's age is 15 years and Gita's age is 25 years.

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Let's understand a few concepts:

Let's say "x" years be the present age of a person.

We have "n" no. of years.

So,

The person's age after n years will be = (x + n) years

and

The person's age n years ago / n years back was = (x - n) years

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Let's solve the given problem:

The ratio of ages of Sita and Gita is 3 : 5.

So, let's say

"3x" years → Sita's age

"5x" years → Gita's age

After 5 years:

Sita's age will be = (3x + 5) years

Gita's age will be = (5x + 5) years

The new ratio of their ages after 5 years = 2 : 3

Therefore, we can form an equation as,

$\frac{3x \:+\:5}{5x \:+\:5} = \frac{2}{3}$

$\implies 3(3x + 5) = 2(5x + 5)$

$\implies 9x + 15 = 10x + 10$

$\implies 10x - 9x = 15 - 10$

$\implies \bold{x = 5}$

Now,

Sita's age = $3x = 3\times 5 = \bold{15 \:years}$

and

Gita's age = $5x = 5\times 5 = \bold{25 \:years}$

Thus, their ages are 15 years and 25 years.

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Answer 2

Information provided with us :

• The ages of Sita and Gita are in the ratio 3:5.
• After 5 years, their ratio will become 2:3.

What we have to calculate :

• Ages of Sita and Gita ?

Performing Calculations :

Here this is the concept of linear equations. As we know that, in linear equations we assumes unknown number as an variable. Here also we would be doing same. But we would be assuming a common factor for ages of Sita and Gita because we've been given with the ratio of their ages. So let us assume the common factor as k.

★ Therefore,

• Age of Sita = 3 × k = 3k
• Age of Gita = 5 × k = 5k

★ According to the question,

It is also given that after five years their ratio will become 2 : 3.

So after five years there ages would be,

• Age of Gita = 3k + 5
• Age of Sita = 5k + 5

So we would be keeping this ratio (2:3) it equal to the ages of Sita and Gita which we got after five years.

$\implies \: \sf{ \dfrac{3k + 5}{5k + 5} \: = \: \dfrac{2}{3} }$

Cross multiplying them,

$\implies \: \sf{ 3(3k + 5)\: = \: 2(5k + 5)}$

$\implies \: \sf{ 3 \times (3k + 5)\: = \: 2 \times (5k + 5)}$

$\implies \: \sf{ 9k + 15\: = \: 10k + 10}$

Transposing 10k from R.H.S. to L.H.S.,

$\implies \: \sf{ 9k - 10k + 15\: = \: 10}$

Now transposing 15 from L.H.S. to R.H.S.,

$\implies \: \sf{ 9k - 10k\: = \: 10 - 15}$

$\implies \: \sf{ - 1k\: = \: 10 - 15}$

$\implies \: \sf{ - 1k\: = \: - 5}$

$\implies \: \red{\boxed{\bf{k\: = \: 5}}}$

Therefore, value of k is 5.

★ Finding out age of Sita:-

$\implies \: \tt{Age \: of \: Sita \: = \: 3k}$

$\implies \: \tt{Age \: of \: Sita \: = \: 3 \times 5}$

$\implies \: \tt{Age \: of \: Sita \: = \: 15}$

★ Finding out age of Git:-

$\implies \: \tt{Age \: of \: Gita \: = \: 5k}$

$\implies \: \tt{Age \: of \: Gita \: = \: 5\times 5}$

$\implies \: \tt{Age \: of \: Gita \: = \: 25}$

Henceforth,

• Ages of Sita and Gita are 15 and 25 years respectively.