Question

I am three times as old as my sister. Nine years later, i shall be one and half times as old as my sister. What is my present age?​

Answer 1

Question

I am three times as old as my sister. Nine years later, I shall be one and half times as old as my sister. What is my present age ?

Answer

Your present age would be 9 years .

Solution

Let your sister's age be x yrs and your age then should be 3x yrs. [You're three times as old as your sister]

Now, Nine years later according to the equation

Your Sister age would be = (x+9) yrs

Your age would be = (3x+9) yrs

According to the question

Nine years later, I shall be 1½ yrs as old as my sister.

Here, we got the equation

$\rightarrow \sf(3x + 9) = \dfrac{3}{2}(x + 9)$

$↦\rm3x + 9 = \dfrac{3}{2}x + \dfrac{27}{2}$

$↦ \rm3x - \dfrac{3x}{2} = \dfrac{27}{2} - 9$

$↦ \rm \dfrac{6x - 3x}{2} = \dfrac{27 - 18}{2}$

$↦ \rm \dfrac{3x}{ \cancel2} = \dfrac{9}{ \cancel2}$

$↦ \rm \: 3x = 9$

$↦ \rm x = \cancel\dfrac{9}{3} = 3$

Hence, we get the value for x i.e 3 yrs ( your sister's age) and thus your present age is assumed to be 3x yrs = 3 × 3 = 9 years

Conclusion

Your present age is , thus , 9 years.

$\underline{\rule{190pt}{2pt}}$

✎ Note

In the above question it is given that you would be 1½ times as old as your sister this means that you would be 3/2 years then your sister.

Thankyou