Time and work

Story hook

Imagine two friends, Ravi and Sara, decide to paint the back wall of their school for a holiday project.

Ravi is quick. If he paints all alone, he can finish the whole wall in 4 days. Sara is a little slower — alone she would take 6 days to finish the same wall.

Now here is the interesting bit. On the actual day, both of them paint together, side by side, dipping their brushes at the same time. The big question everyone in the class is asking is:

If Ravi alone needs 4 days and Sara alone needs 6 days, how many days will the two of them take working together?

A very common first guess is "the average, so 5 days." But wait — if two people work together, they should finish faster than either one alone, not slower than Ravi's 4 days! So 5 days cannot be right.

The real answer turns out to be 2 days and a bit — quicker than even Ravi. By the end of this lesson you will be able to find that number in about twenty seconds, and you will understand exactly why it works. We start from absolute zero. Take a breath and follow along.

Why this matters for UPSC

For your CSAT exam (UPSC Prelims Paper II):

• CSAT is a qualifying paper — you do not need a brilliant score. You only need 33% (that is 66 marks out of 200) to pass. Time-and-work questions appear almost every year, and once you know the small set of ideas here, they become reliable, quick marks.
• Most of these questions are solved by one clean idea (turn days into "work per day" and add). That makes them fast — often a 20–40 second job. Exactly the kind of safe mark you want to bank early.

For real life (this is the fun part):

• When your family plans a task — cleaning the whole house before Diwali, say — you can work out how long it takes if everyone pitches in together.
• When a team builds something (a wall, a garden bed, a school banner), you can estimate the finish time before you even start.
• You learn to spot a sneaky thing: adding more people does NOT always halve the time in the way people guess — you will know the real numbers.
• It trains a calm habit: turn a confusing word problem into one small, steady rate, and the rest follows.

So this is not only an exam topic — it is everyday planning sense. And it all grows from one tiny idea: think of a job as "1 whole," and ask how much of it gets done in a single day. Let's begin.