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

(d) 9 years

Mr. Manoj's age be (10x + y) yrs. 

Then, his wife's age = (10y + x) years 

Given,

\(\frac{1}{11}\)(10x + y + 10y + x) = (10x + y) – (10y + x)

\(\Rightarrow\)\(\frac{1}{11}\)(11x +11y) = 9x -9y

\(\Rightarrow\)x + y = 9x – 9y

\(\Rightarrow\)8x = 10y

\(\Rightarrow\)\(\frac{X}{y}\) = \(\frac{5}{4}\)

\(\therefore\) x = 5, y = 4 (because any other multiple of 5 will make x two digits)

\(\therefore\) Difference = 9x – 9y = 9 (x – y) = 9 (5 – 4) = 9 yrs.