Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is:

Question

Accepted Answer

1. **Given Data**:
   - Gautam and Suhani together can complete the job in 20 days.
   - Gautam works at 60% of his capacity while Suhani works at 150% of her capacity to balance the work.

2. **Relation Between Their Efficiencies**:
   - When Gautam does 60% of his work, Suhani compensates by doing 150% of her work.
   - This implies that 40% of Gautam's work equals 50% of Suhani's work.
   - Therefore, $$ 	ext{Gautam’s efficiency} = 1.25 	imes 	ext{Suhani’s efficiency}. $$

3. **Let Suhani’s Time to Complete the Job Alone Be $$ x $$ Days**:
   - Suhani’s rate of work per day = $$ \frac{1}{x} $$.
   - Gautam’s rate of work per day = $$ \frac{1.25}{x} $$.

4. **Combined Work Rate**:
   - Together, they complete the job in 20 days.
   - Combined rate = $$ \frac{1}{20} $$.
   - Hence,
     $$
     \frac{1}{x} + \frac{1.25}{x} = \frac{2.25}{x} = \frac{1}{20}.
     $$

5. **Solve for $$ x $$**:
   $$
   \frac{2.25}{x} = \frac{1}{20}.
   $$
   $$
   x = 20 	imes 2.25 = 45.
   $$
   So, Suhani alone can complete the job in **45 days**.

6. **Time Taken by Gautam Alone**:
   - Since Gautam is 1.25 times faster than Suhani:
     $$
     	ext{Gautam’s time} = \frac{x}{1.25} = \frac{45}{1.25} = 36 \, 	ext{days}.
     $$

Thus, the faster worker (Gautam) would take **36 days** to complete the job alone.