Question

What is Sonia's present age?
I. Sonia's present age is five times Deepak's present age.

II. Five years ago her age was twenty-five times Deepak's age at that time.

• A. I alone sufficient while II alone not sufficient to answer
• B. II alone sufficient while I alone not sufficient to answer
• C. Either I or II alone sufficient to answer
• D. Both I and II are not sufficient to answer
• E. Both I and II are necessary to answer

Answer 1

Answer: (E)

Both I and II are necessary to answer

Let Sonia's present age be '$S$' years and that of Deepak's be '$D$' years.

$\therefore S=5D$ [From I] ....... (i)

Now their respective ages five years ago will be , $(S-5)$ and $(D-5)$ years.

$\therefore S-5=25(D-5)\Rightarrow S-5=25D-125\Rightarrow S=25D-120$ [From II]....(ii)

Now substituting the value of $S$ from (i)in (ii),we get,

$\Rightarrow 5D=25D-120$

$\Rightarrow 5D-25D=-120$

$\Rightarrow 20D=120$

$\Rightarrow D=6$ years

$\therefore S=5\times 6=30$ years

Thus, we can say that, Both I and II are necessary to answer the question.