Problems on ages

Story hook

It is your birthday. Your grandmother smiles, holds your hand, and says: "When you were born, I was already fifty years old!"

You think for a moment. You are turning 10 today. So how old is grandma now?

You do a little sum in your head: she was 50 when you were 0, and you have grown 10 years since then, so she has also grown 10 years. That means grandma is 50 + 10 = 60 today.

Look at the lovely thing that just happened. You did not need to ask grandma her age. You worked it out from a clue! And here is the secret that makes all age puzzles easy:

Everybody in the world grows older by the same amount of time at the same time. If 10 years pass for you, 10 years pass for grandma too. The gap between two people's ages never changes.

In this lesson we will turn age puzzles into easy little sums. We will learn to call an unknown age x, write ages in the past and future, use ratios of ages, and turn a sentence into one simple equation. We start from absolute zero. Take a breath, grab a pencil, and let's begin.

Why this matters for UPSC

For your CSAT exam (UPSC Prelims Paper II):

• CSAT is a qualifying paper. That means you do not need a top score — you only need 33% (that is 66 marks out of 200) to pass. Age problems are one word and one equation away from a tick mark, so they are perfect for safely collecting those qualifying marks.
• They look like a riddle but follow a fixed recipe. Once you learn the recipe ("call it x, write the sentence as an equation"), almost every age question becomes the same friendly sum.

For real life (this is the fun part):

• Family ages — working out how old a cousin, parent or grandparent is from a clue ("Dad is twice my age").
• Birthday and anniversary maths — "In how many years will I be 18?", "How old was mum when I was born?"
• Puzzles and quizzes that friends love to ask ("Guess my age, it is 3 times my son's age...").
• Reading old documents — "She joined work at 21, retired after 38 years — how old was she then?"

So this is not just an exam topic. It is the everyday maths of birthdays, families and clever riddles. And it begins as simply as working out grandma's age. Stay relaxed and follow each step.