Question

Five years ago pooja was twice sanchi's age. five years hence, their age will be in the ratio 4:3. find their present ages?

Answer 1

Let us assume, x is the present age of Pooja and y is the present age of Sanchi.

Given, 5 years ago,

x - 5 = 2 (y - 5)
x - 5 = 2y - 10
2y - x = 5 -----------------1

Also given, 5 years hence, the ratio of their ages = 4:3

Therefore, (x + 5) : (y + 5) = 4:3
(x + 5) / (y + 5) = 4/3
3 (x + 5) = 4 (y + 5)
3x + 15 = 4y + 20
3x - 4y = 5 -----------------2

Multiply equation 1 by 3

6y - 3x = 15 --------------3

Adding equation 2 and equation 3

2y = 20
y = 10 years

Substitute the value of y in equation 1

2y - x = 5
2 * 10 - x = 5
20 - x = 5
x = 15 years

The present age of Pooja is 15 years and present age of Sanchi is 10 years.

Answer 2

Answer:

SOLUTION

Let the Sanchi 5years ago=x years

Let the Sanchi 5years ago=x yearsThen the age of puja 5years ago=2x yrs

Now present age of Sanchi=(x+5) years

Present age of Pooja= (2x+5) years

Five years ago:

Sanchi's age = (x+10) years

Pooja age = (2x+10) years

Now,

\begin{gathered}= > \frac{2x + 10}{x + 10} = \frac{4}{3} \\ \\ = > 3(2x + 10) = 4(x + 10) \\ = > 6x + 30 = 4x + 40 \\ = > 6x - 4x = 40 - 30 \\ = > 2x = 10 \\ = > x = \frac{10}{2} = 5\end{gathered}

=>

x+10

2x+10

=

3

4

=>3(2x+10)=4(x+10)

=>6x+30=4x+40

=>6x−4x=40−30

=>2x=10

=>x=

2

10

=5

So, present age of Sanchi = 5+5= 10yrs.

Present of pooja age= 2(5)+5 = 10+5

=) 15 years

hope it helps ☺️