2. Time and Work

Medium Acceptance: 62.1%

A can complete a piece of work in 15 days, and B can complete the same work in 20 days. They work together for 4 days, then A leaves the job. In how many days will B complete the remaining work?

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Time and Work Quantitative Aptitude

Medium

A can complete a piece of work in 15 days, and B can complete the same work in 20 days. They work together for 4 days, then A leaves the job. In how many days will B complete the remaining work?

Interactive Visual Explanation

Step 1 of 4

Step 1

Find Total Work (LCM Method)

Find the Least Common Multiple (LCM) of the days taken by A and B to represent the Total Work as discrete units. LCM of 15 and 20 is 60 units.

LCM Units Model (60 Total Work Blocks) Click segments below to filter phases

A's Work (4 units/day × 4 days = 16 blocks)

B's Work (3 units/day × 4 days = 12 blocks)

B's Solo Remaining Work (32 blocks)

\text{Total Work} = 60 \text{ units}

Step 2

Calculate Individual Efficiencies

Work efficiency represents the amount of work completed in 1 day.
- Efficiency of A = 60 / 15 = 4 units/day.
- Efficiency of B = 60 / 20 = 3 units/day.

\text{Combined Efficiency} = 4 + 3 = 7 \text{ units/day}

Step 3

Calculate Work Completed in 4 Days

Since they work together for 4 days, they complete: Combined Efficiency × 4 days = 28 units.

7 \text{ units/day} \times 4 \text{ days} = 28 \text{ units}

Step 4

Find Remaining Days for B

The remaining work is: Total Work - Completed Work = 60 - 28 = 32 units. B must do this work alone at their efficiency of 3 units/day:

\text{Remaining Days} = \frac{32 \text{ units}}{3 \text{ units/day}} = 10\frac{2}{3} \text{ days}

⚡

CGL Exam Speed Trick

⚡ LCM Shortcut: The LCM method prevents you from adding fractions like $1/15 + 1/20$, which is slow and error-prone. Master finding LCMs in your head (e.g. 20, 40, 60... 60 divides 15. Got it!) to solve Time & Work in under 30 seconds.

⚡ Speed-Run CGL Cheatsheet

Mastering these core principles will let you solve similar questions under 30 seconds.

Core Identity:

Total Work = LCM(Individual Days)

Check the interactive visualizer in the first tab to see these formulas modeled geometrically!

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