Lesson 1.7: Time, Work, Wages

Introduction:
Time, Work, and Wages problems are common in SSC exams. These problems test your ability to calculate work done, efficiency, and wages based on work completed.

1. Time and Work

• Definition: Work = Rate × Time

• Basic Formula:

$$\text{Work Done}=\text{Efficiency}\times \text{Time}$$ Time=WorkEfficiency\text{Time} = \frac{\text{Work}}{\text{Efficiency}}Time=EfficiencyWork​

• Example 1:
  A can complete a work in 10 days. How much work will A complete in 4 days?

Work done=410=2/5 of total work\text{Work done} = \frac{4}{10} = 2/5 \text{ of total work}Work done=104​=2/5 of total work

• Combined Work:
  If A can do a work in 10 days, B in 15 days, work together:

1 day’s work=110+115=16\text{1 day’s work} = \frac{1}{10} + \frac{1}{15} = \frac{1}{6} 1 day’s work=101​+151​=61​

Time to finish = 6 days

2. Efficiency

• Definition: Efficiency = Work done per day

• Relation:

$$\text{Efficiency}\propto \text{Work done in a day}$$

• Example 2:
  A is twice as efficient as B. If B can finish a work in 12 days, A can finish in:

$$12/2=6\text{ days}$$

3. Wages

• Definition: Wages are directly proportional to work done.

$$\text{Wages}=\text{Rate × Work done}$$

• Example 3:
  A and B complete a work together. Total wages = ₹1,200. Work ratio A:B = 2:3.

• A’s share = (2/5) × 1200 = ₹480

• B’s share = (3/5) × 1200 = ₹720

4. SSC Exam Tips

• Use unitary method for quick calculation.

• Convert all efficiencies to same units (work/day or work/hour).

• For combined work problems, always calculate 1 day’s work first.

• Wages problems usually appear in CHSL and MTS exams.

5. Practice Questions

1. A can complete a work in 12 days, B in 18 days. Find time to complete together.

2. A is 3 times as efficient as B. B can do a work in 15 days. Find A’s time.

3. Two workers complete a work. Total wages = ₹900. Their work ratio = 3:2. Find each share.

4. If A, B, C can do a work in 10, 15, and 20 days respectively. Time to complete together?

5. A alone can complete a work in 8 days. He works 3 days, then B finishes the remaining in 4 days. Find B’s efficiency relative to A.