Shyam can do a job in 20 days, Ram in 30 day and Singhal in 60 days. If Shyam is helped by Ram and Singhal every 3rd day how many days will it take for them to complete the job?

Options

A. 12
B. 16
C. 15
D. 10

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Determine the work done by each person in one day.
- Shyam can complete the job in 20 days. Therefore, his work per day = \( \frac{1}{20} \) of the job.
- Ram can complete the job in 30 days. Therefore, his work per day = \( \frac{1}{30} \) of the job.
- Singhal can complete the job in 60 days. Therefore, his work per day = \( \frac{1}{60} \) of the job.

### Step 2: Calculate the total work done in units.
To make calculations easier, we can assume the total work is represented by the least common multiple (LCM) of the days taken by Shyam, Ram, and Singhal:
- LCM of 20, 30, and 60 is 60 units of work.

### Step 3: Calculate the work done by each person in terms of units.
- Work done by Shyam in one day = \( \frac{60}{20} = 3 \) units.
- Work done by Ram in one day = \( \frac{60}{30} = 2 \) units.
- Work done by Singhal in one day = \( \frac{60}{60} = 1 \) unit.

### Step 4: Determine the work cycle.
Shyam works alone for 2 days and is assisted by Ram and Singhal on the 3rd day.
- Work done by Shyam in 2 days = \( 3 \text{ units/day} \times 2 \text{ days} = 6 \text{ units} \).
- Work done by Shyam, Ram, and Singhal together on the 3rd day = \( 3 + 2 + 1 = 6 \text{ units} \).

### Step 5: Calculate the total work done in one complete cycle of 3 days.
- Total work done in 3 days = Work done in 2 days by Shyam + Work done on the 3rd day by all three = \( 6 + 6 = 12 \text{ units} \).

### Step 6: Determine how many cycles are needed to complete the job.
- Total work required = 60 units.
- Work done in one cycle (3 days) = 12 units.
- Number of cycles needed = \( \frac{60 \text{ units}}{12 \text{ units/cycle}} = 5 \text{ cycles} \).

### Step 7: Calculate the total time taken.
- Each cycle takes 3 days.
- Total time taken = Number of cycles × Days per cycle = \( 5 \times 3 = 15 \text{ days} \).

### Final Answer:
It will take a total of **15 days** for Shyam, Ram, and Singhal to complete the job.

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