Question

If the two digits of the ages of Mr. Manoj are reversed then the new age so obtained is the age of his wife. $\frac{1}{11}$ of the sum of their ages is equal to the difference between their ages. If Mr. Manoj is elder than his wife, then find the difference between their ages.

• A. $10$ years
• B. $8$ years
• C. $7$ years
• D. $9$ years

Answer 1

The correct option is D $9$ years

Let us take Monoj's age$=10x+y.$

Then, his wife's age$=10y+x.$

The sum of their ages$=10x+10y+10y+x=11(x+y)$.

The difference of their ages$=10x+y-10y-x=9x-9y$

$\frac{1}{11}\times 11(x+y)=9x-9y\Rightarrow (x+y)=9(x-y)\Rightarrow 8x=10y\Rightarrow \frac{x}{y}=\frac{10}{8}=\frac{5}{4}$

Now, any other multiple of $5$ will make it double digit, which is impossible ( x & y are single digits).

So, $x=5$ & $y=4.$

$\therefore$ The difference of their ages will be

$9(x-y)=9(5-4)yrs=9$ yrs.