Question

What is Mohan’s age?
Statements: (i) In $15$ years, Mohan will be twice as old as Ram would be.
(ii) Ram was born $5$ years ago.
A. Only I is sufficient
B. Only II is sufficient
C. Both I and II are required
D. Both I and II are not sufficient

Answer 1

Hint:The application of the concept of logical reasoning and apply logic to determine the age of Mohan. The present year is taken into consideration and also the age difference between Ram’s age and the predicted Mohan’s age in $15$ years must be kept in track and found out in order to calculate the age accurately and also determine whether both statements are required or not.

Complete step by step answer:
The above problem revolves around the concept of basic mathematics and logical reasoning which is required to be applied in order to find Mohan’s age. The question mentions two people namely, Mohan and Ram whose ages are said to be related to each other. We are required to predict or calculate the age of Mohan from the data given about Ram’s age. To do this we must construct an equation relating both their ages so that Mohan’s age can be found out.

The first statement tells us what the age of Mohan will be in $15$ years from the current year which is presently running, with respect to Ram’s age. The second statement tells us when Ram was born which is given to be $5$ years before, that is, $5$ years back from the present year that is running.

The first statement gives us the future information about their ages and the second statement gives us the past data, that is, Ram was born $5$ years ago. A point to consider here is that both the statements give data from the present year which is running.

Let us now look at the first statement. It says that Mohan’s age will be twice that of Ram’s age after $15$ years from now, that is, the current year. Let us now look at the second statement. It mentions that Ram was born $5$ years ago from the current year. This means that in order to calculate Mohan’s age with respect to Ram’s age we need to take into consideration the extra five years to equate Ram’s age with Mohan’s age.

We need to add the $5$ years along with the $15$ years of time period that we are taking into consideration from statement I because we are trying to equate the ages of both of them. So as per the data of statement I the age of Mohan after $15$ years will be twice the age of Ram. Hence after $15$ years Mohan’s age will be given by the equation:
$ \Rightarrow 2 \times (5 + 15)$

But however we need the present age of Mohan and hence the present year must be taken into consideration which will be $15$ years back to get back to the current year again. Hence, for finding Mohan’s current age we need to subtract $15$ years from the above equation since the above equation is given as the age of Mohan $15$ years later.Thus, we get:Mohan’s age $ = 2 \times (5 + 15) - 15$

By solving this equation in accordance with the principles of BODMAS we get Mohan’s age. According to BODMAS brackets should be solved first and hence we get:
Mohan’s age $ = 2 \times (20) - 15$
Next, the multiplication operation has more importance than subtraction and hence we get:
Mohan’s age $ = 40 - 15$
On further simplification we get:
Mohan’s age$ = 25\;years$
Therefore, this is the current age of Mohan as he is said to be $25$ years old. As it can be clearly seen that this could only be determined with the help of both the statements I and II since the combination of them was applied to find out Mohan’s age.Hence, both statements, I and II are required in order to find out Mohan’s age.

Therefore, the correct option is option C.

Note:The most common error that is made in these sort of problems is that the extra $5$ years is missed to be added to the $15$ years as the age difference or the age gap between them is not considered which is incorrect. The correct construction of the equation for the age difference between them is not made generally.