Rajeev age after 15 years will be 5 times his age 5 years ago. What is the present age of Rajeev in years?

Introduction / Context:
This problems-on-ages question relates Rajeev age at two different points in time: 5 years ago and 15 years in the future. The relation given is multiplicative, meaning the future age is a multiple of the past age. The goal is to translate this into an equation and compute Rajeev present age.

Given Data / Assumptions:

• Rajeev age after 15 years will be 5 times his age 5 years ago.
• We are asked to find his current age.
• All ages are in years and considered positive.

Concept / Approach:
When a relationship involves a person age at two different times, we first express both of those ages in terms of the present age. Then we use the given multiplicative relationship to write a single equation. Solving that equation yields the present age. This is a basic application of linear equations in one variable.

Step-by-Step Solution:
Let the present age of Rajeev be A years.His age 5 years ago was A - 5 years.His age after 15 years will be A + 15 years.The condition says: age after 15 years = 5 times age 5 years ago.So we write: A + 15 = 5 * (A - 5).Expand the right side: A + 15 = 5 * A - 25.Rearrange terms: Move A to the right and -25 to the left.15 + 25 = 5 * A - A.40 = 4 * A.So A = 40 / 4 = 10 years.

Verification / Alternative check:
If Rajeev is 10 now, then 5 years ago he was 10 - 5 = 5 years old.15 years from now he will be 10 + 15 = 25 years old.Check the relationship: 25 is indeed 5 times 5.Thus, the condition is perfectly satisfied for A = 10 years.

Why Other Options Are Wrong:
12 years: If A = 12, then A - 5 = 7 and A + 15 = 27. Here 27 is not 5 times 7.14 years: If A = 14, then A - 5 = 9 and A + 15 = 29, and 29 is not 5 times 9.22 years: If A = 22, then A - 5 = 17 and A + 15 = 37, which again does not satisfy the relationship.

Common Pitfalls:
Students sometimes interchange the time intervals and write A - 15 and A + 5, which mixes up past and future ages.Misplacing terms while rearranging the equation can lead to incorrect values of A.Occasionally, learners confuse five times with increasing by 5, which is a completely different relationship.

Final Answer:
The present age of Rajeev is 10 years.