Aptitude Preparation for Placements Lesson 2 of 29

Time and Work

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Hello friends, welcome to shrash studio learning, in this article we start Time and Work for placement aptitude. Company tests love this topic. We focus on one clear idea: how much work is done in one day. Once that clicks, most questions become easy.

The Main Idea

Think of the full job as 1 whole work (like one full pizza = 1).

If someone finishes the job in 2 days, then in one day they finish half of the work. We write that as 1/2 per day.

If someone finishes the same job in 3 days, then in one day they finish one-third. We write 1/3 per day.

Rule: If a person finishes work in D days, then in one day they do 1/D of the work.

Example 1 — Two People Working Together

Question: A can finish a task in 2 days. B can finish the same task in 3 days. How many days if they work together?

Step 1 — One day work:

Person Finishes full work in Work done in 1 day
A 2 days 1/2
B 3 days 1/3

Step 2 — Together in one day: Add the parts.

1/2 + 1/3 = 3/6 + 2/6 = 5/6 of the work in one day.

Step 3 — Days needed: If 5/6 is done in 1 day, then full work (1) needs:

1 ÷ (5/6) = 6/5 days = 1.2 days

So together they take 6/5 days (same as 1 day and a bit — placement answers often leave it as a fraction).

Example 2 — Many People, Same Speed

Question: One man finishes a wall painting in 15 days. If 5 men work together (each same speed), how many days?

One man does 1/15 per day.

Five men do 5 × (1/15) = 5/15 = 1/3 per day.

Full work in 1 ÷ (1/3) = 3 days.

If each person is equally fast: n people do n × (one person’s one-day work) in a day.

Example 3 — Total Work as LCM (Trick for “Different Days”)

Sometimes the numbers are ugly for fractions. Then assume total work = LCM of the given days. It is still the same math — just easier numbers.

Question: A finishes in 4 days, B in 6 days. Together?

LCM of 4 and 6 is 12. Pretend the task has 12 units.

Using 12 units of work
A: 12 units in 4 days → 12÷4 = 3 units per day
B: 12 units in 6 days → 12÷6 = 2 units per day
Together: 3 + 2 = 5 units per day
Time: 12 ÷ 5 = 12/5 days

Same answer as adding fractions — pick the style you like in the exam.

Example 4 — Men and Boys (Very Common Type)

Question: 12 men can finish a job in 20 days. How much does one man do in one day?

Treat total work as 1.

12 men together finish 1/20 of the work per day.

So one man per day = (1/20) ÷ 12 = 1/(20×12) = 1/240 of the full work.

If the paper says “6 boys equal 12 men” or similar, you first convert everyone to “man-days” or use the same fraction idea — always come back to work per day.

Example 5 — Some Days Together, Some Days Alone

Question (story style): Total work is 1. A+B together do 1/6 per day. They work together for 2 days, then only A works alone and he does 1/12 per day. How much work is left after 2 days together?

Together in 2 days: 2 × (1/6) = 1/3 done.

Remaining work: 1 − 1/3 = 2/3.

Then A finishes the rest at 1/12 per day — days needed = (2/3) ÷ (1/12) = 8 days. (Small algebra step: dividing by a fraction = multiply by flip.)

In exams the numbers change, but the story is always: add what got done, subtract from total, then use one-day work for the rest.

Quick Formula Sheet

Situation What to do
Finishes in D days One-day work = 1/D
A and B together Add their one-day parts
n same-speed workers Multiply one person’s one-day part by n
Time from combined rate R Days = 1 ÷ R
Messy denominators Use total work = LCM of days, count “units per day”

Mistakes Students Make

AVOID THESE

Adding days wrong

You don’t add “2 days + 3 days” for together time. You add daily work.

Forgetting “same work”

Everyone must be finishing the same job unless the question says otherwise.

Rushing units

If men and boys differ, convert to one type before adding rates.

Practice (Try Yourself)

These are for you — answers at the end.

# Question
1 P finishes work in 5 days, Q in 10 days. Together — how many days?
2 8 workers finish a task in 6 days. How long for 12 workers (same speed)?
3 Total work = 60 units. A does 5/day, B does 4/day. Together — days?

Answers: (1) 10/3 days  |  (2) 4 days  |  (3) 60÷9 = 20/3 days.

Summary

Time and Work is mostly about work done in one day. Finish in 2 days → 1/2 per day; finish in 3 days → 1/3 per day. Together → add daily parts. Many workers same speed → multiply one person’s daily part. Hard numbers → use total work as LCM and count units per day. Men/boys → convert fairly, then same rules.

Practice a few questions daily with a timer — that is how this topic becomes automatic in the exam hall.

Idea Remember
Core rule One-day work = 1 ÷ (days to finish alone)
Together Add one-day works; total days = 1 ÷ sum
More people Same speed → multiply rate by headcount
LCM trick Total units = LCM of individual days
Story sums Track finished part, subtract from 1, finish rest
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