Question

Rohan was 7 years old when Sohan was born. Rohan said to Sohan, "I'm twice as old as you were when I was as old as you are." Find their present ages.

Answer 1

The problem is solved using algebra. Rohan is currently 28 years old and Sohan is 21 years old, found by setting up equations based on the given relationships and solving for the unknowns.

Step-by-step explanation:

The question posed is a classic age-related puzzle. To solve for Rohan and Sohan's present ages, let us use algebra. Let's denote Rohan's current age as R and Sohan's current age as S. Since Rohan is 7 years older than Sohan, we can express Rohan's age when Sohan was born as R = S + 7. According to Rohan's statement 'I'm twice as old as you were when I was as old as you are,' we understand that when Rohan was Sohan's current age (S years old), Sohan was younger.

We need to express the time passed since Rohan was Sohan's current age, which is R - S years. At that time, Sohan's age would have been S - (R - S) or 2S - R. Now, the present age of Rohan is twice this value, so we set up the following equation: R = 2(2S - R). Substituting R = S + 7 into this equation gives us:

R = 2(2S - (S + 7))
R = 2(S - 7)
S + 7 = 2S - 14
7 + 14 = 2S - S
21 = S

So, Sohan's current age is 21 years old. To find Rohan's current age, we substitute S into the first equation:

R = S + 7
R = 21 + 7
R = 28

Therefore, Rohan is 28 years old and Sohan is 21 years old.

Answer 2

Rohan is currently 28 years old and Sohan is currently 21 years old.

Let's denote Rohan's current age as R and Sohan's current age as S. The given information can be expressed through the following statements:

Rohan was 7 years old when Sohan was born, so when Sohan was born, Rohan's age was R - S = 7.

Rohan said to Sohan, "I'm twice as old as you were when I was as old as you are." This can be translated into the equation: R = 2 imes (S - (R - S)).

Now, let's solve these equations to find their present ages:

From equation (1): R - S = 7. So, R = S + 7.

Substitute this into equation (2): S + 7 = 2 imes (S - 7).

Simplify the equation: S + 7 = 2S - 14.

21 = S.

So, Sohan is currently 21 years old. Now, substitute S = 21 back into R = S + 7:

R = 21 + 7 = 28.

Therefore, Rohan is currently 28 years old.