Question

Two years ago, Kirti was four times as old as her
daughter Sunidhi. Ten years hence, Kirti will be two
times as old as her daughter. Find the ratio of the
present ages of Kirti and her daughter.​

Answer 1

Step-by-step explanation:

The ratio of present ages of Kirti and her daughter Sunidhi is 13:4

Answer 2

The ratio of the  present ages of Kirti and her daughter Sunidhi is $\frac{13}{4}$.

Step-by-step explanation:

Let the present age of Kirti be 'x'.

And let the present age of Sunidhi be 'y'.

Two years ago age of Kirti = $(x-2)\ yrs$

Two years ago age of Sunidhi = $(y-2)\ yrs$

Now, According to question, two years ago, Kirti was four times as old as her

daughter Sunidhi.

We can frame it in equation form as;

$(x-2)=4(y-2)\\\\x-2=4y-8\\\\4y-x=-2+8\\\\4y-x=6\ \ \ \ \ equation\ 1$

After ten years ago age of Kirti = $(x+10)\ yrs$

After ten years ago age of Sunidhi = $(y+10)\ yrs$

Again, According to question, Kirti will be two  times as old as her daughter Sunidhi.

We can frame it in equation form as;

$(x+10)=2(y+10)\\\\x+10=2y+20\\\\x-2y=20-10\\\\x-2y=10\ \ \ \ equation\ 2$

Now adding equation 1 and equation 2, we get;

$(4y-x)+(x-2y)=6+10\\\\4y-x+x-2y=16\\\\2y=16\\\\y=\frac{16}{2}=8$

Putting the value of 'y' in equation 1, we get;

$4y-x=6\\\\4\times8-x=6\\\\32-x=6\\\\x=32-6=26$

Thus the present age of Kirti is 26 yrs and of Sunidhi is 8 yrs.

$Ratio=\frac{26}{8}=\frac{13}{4}$

Hence The ratio of the  present ages of Kirti and her daughter Sunidhi is $\frac{13}{4}$.