Rohan and Rohit together can do a certain job in 10 days while Rohan alone can do the same job in 15 days. How many days Rohit alone will do the same job?
(a)25 days
(b)32 days
(c)35 days
(d)30 days

Options

A. 25 days
B. 32 days
C. 35 days
D. 30 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Work Done
Rohan and Rohit together can complete a job in 10 days. This means that in one day, they complete \( \frac{1}{10} \) of the job.

### Step 2: Calculate Their Combined Work Rate
If we assume the total work is 30 units (for easier calculation), then:
- In 10 days, they complete 30 units.
- Therefore, their combined work rate is \( \frac{30 \text{ units}}{10 \text{ days}} = 3 \text{ units per day} \).

### Step 3: Calculate Rohan's Work Rate
Rohan alone can complete the job in 15 days. Thus, his work rate is:
- \( \frac{30 \text{ units}}{15 \text{ days}} = 2 \text{ units per day} \).

### Step 4: Find Rohit's Work Rate
Now, we know the combined work rate of Rohan and Rohit is 3 units per day, and Rohan's work rate is 2 units per day. We can find Rohit's work rate by subtracting Rohan's work rate from their combined work rate:
- Rohit's work rate = Combined work rate - Rohan's work rate
- Rohit's work rate = \( 3 \text{ units/day} - 2 \text{ units/day} = 1 \text{ unit/day} \).

### Step 5: Calculate How Long Rohit Takes to Complete the Job Alone
If Rohit can do 1 unit of work in one day, then to complete the entire job of 30 units, he will take:
- Time = Total Work / Rohit's Work Rate
- Time = \( \frac{30 \text{ units}}{1 \text{ unit/day}} = 30 \text{ days} \).

### Conclusion
Thus, Rohit alone will take **30 days** to complete the job.

### Answer
(d) 30 days

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