Question

x years ago, the difference between the ages of Hari and Sadu was y years. Then after z years what will be the difference between their ages.
A) x years
B) y years
C) z years
D) $\left( {x + y + z} \right)$ years

Answer 1

Hint: First assume the present age of Hari and Sadu. After that, subtract x from both ages to get the ages of Hari and Sadu x years ago. Then, find the subtract of the age of Sadu from the age of Hari and equate it to y. Now add z in both ages to get the ages of Hari and Sadu to get the age after z years. Then again subtract the age of Sadu from the age of Hari and do simplification to get the age difference.

Complete step-by-step answer:
Let the present age of Hari be P years and the present age of Sadu be Q years.
Now, the age of Hari x years ago will be,
$ \Rightarrow \left( {P - x} \right)$ years
The age of Sadu x years ago will be,
$ \Rightarrow \left( {Q - x} \right)$ years
Now subtract the age of Sadu from the age of Hari to get the difference of ages and equate it to y,
$ \Rightarrow \left( {P - x} \right) - \left( {Q - x} \right) = y$
Open the brackets and change the sign accordingly,
$ \Rightarrow P - x - Q + x = y$
Add or subtract the same terms,
$ \Rightarrow P - Q = y$ ………..…. (1)
Now, the age of Hari after z years will be,
$ \Rightarrow \left( {P + z} \right)$ years
The age of Sadu after z years will be,
$ \Rightarrow \left( {Q + z} \right)$ years
Now subtract the age of Sadu from the age of Hari to get the difference of ages,
$ \Rightarrow \left( {P + z} \right) - \left( {Q + z} \right)$
Open the brackets and change the sign accordingly,
$ \Rightarrow P + z - Q - z$
Add or subtract the same terms,
$ \Rightarrow P - Q$
Substitute the values from the equation (1),
$\therefore y$ years.
So, the difference between their ages after z years is y years.

Hence, option (B) is correct.

Note: In order to solve this type of problems related to age, we need to follow the following steps:-
Step 1: Express what we don't know as a variable.
Step 2: Create an equation based on the information provided.
Step 3: Solve for the unknown variable.
Step 4: Substitute our answer back into the equation to see if the left side of the equation equals the right side of the equation and hence, we will get our final result.