Maths-3 Time and Work: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways)

Maths-3 Time and Work: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways)

Time and Work

Core Concept: Work and Efficiency

Work is assumed to be 1 unit

• In most problems, the total work is considered as 1 unit (or 100%).
• If a person completes the work in 5 days, it means they do 1/5 of the work per day.

Efficiency = Work per day

• If A can do a job in 10 days, A’s efficiency is 1/10.
• If B can do the same job in 5 days, B’s efficiency is 1/5.
• Together, A and B can do 1/10 + 1/5 = 3/10 of the work per day.

Basic Formulae

Single Person Work

Q: A can complete a work in 10 days. How much work does A do in 1 day?

Solution:

• Total work = 1 unit
• Time = 10 days
• Work per day = 1/10

Two People Working Together

Q: A can do a job in 10 days, B can do it in 20 days. How long will they take together?

Solution:

• A’s rate = 1/10
• B’s rate = 1/20
• Combined rate = 1/10 + 1/20 = (2 + 1)/20 = 3/20
• Time = 1 ÷ (3/20) = 20/3 days ≈ 6.67 days

One Starts, Another Joins Later

Q: A can do a job in 10 days. B can do it in 5 days. A works alone for 2 days, then B joins. How long to finish?

Solution:

• A’s rate = 1/10
• B’s rate = 1/5
• Work done by A in 2 days = 2 × 1/10 = 1/5
• Remaining work = 1 – 1/5 = 4/5
• Combined rate = 1/10 + 1/5 = 3/10
• Time to finish = 4/5 ÷ 3/10 = (4/5) × (10/3) = 8/3 days ≈ 2.67 days

Formulas & Shortcuts

• If A does work in x days, B in y days → together = xy/(x+y)  days.
• If A does work in x days, B in y days, C in z days → together = xyz/ (xy+yz+zx)
• Wages are divided in ratio of work done (same as ratio of efficiencies).
• For alternate days → take LCM cycle.

Tips to Solve Quickly

• Always assume total work = 1 unit unless otherwise stated.
• Convert days into rate (efficiency).
• Use LCM method when dealing with multiple workers (especially when work is given in units).
• Practice word problems to get familiar with variations