Ganga, Jamuna and Saraswati can do a piece of work. working together, in 1 day. Ganga is thrice efficient as Jamuna and Jamuna takes the twice the number of days as Saraswati takes to do it alone. What is the difference between the number of days taken by Ganga and Saraswati?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we need to establish the relationships between the efficiencies and the time taken by Ganga, Jamuna, and Saraswati.

### Step 1: Define Variables
Let:
- \( S \) = number of days taken by Saraswati to complete the work alone.
- \( J \) = number of days taken by Jamuna to complete the work alone.
- \( G \) = number of days taken by Ganga to complete the work alone.

### Step 2: Establish Relationships
From the problem statement:
1. Jamuna takes twice the number of days as Saraswati:
\[ J = 2S \]
2. Ganga is thrice as efficient as Jamuna. This means if Jamuna takes \( J \) days, Ganga takes \( \frac{J}{3} \) days:
\[ G = \frac{J}{3} = \frac{2S}{3} \]

### Step 3: Calculate Work Done in One Day
The work done by each person in one day is the reciprocal of the number of days taken:
- Work done by Saraswati in one day:
\[ \text{Work by } S = \frac{1}{S} \]
- Work done by Jamuna in one day:
\[ \text{Work by } J = \frac{1}{J} = \frac{1}{2S} \]
- Work done by Ganga in one day:
\[ \text{Work by } G = \frac{1}{G} = \frac{3}{2S} \]

### Step 4: Total Work Done Together
When Ganga, Jamuna, and Saraswati work together, their combined work done in one day is:
\[ \text{Total Work} = \frac{1}{S} + \frac{1}{2S} + \frac{3}{2S} \]
Combining these fractions:
\[ \text{Total Work} = \frac{1}{S} + \frac{1 + 3}{2S} = \frac{1}{S} + \frac{4}{2S} = \frac{1}{S} + \frac{2}{S} = \frac{3}{S} \]

### Step 5: Set Total Work Equal to 1
Since they can complete the work together in one day:
\[ \frac{3}{S} = 1 \]
This implies:
\[ S = 3 \text{ days} \]

### Step 6: Find Days Taken by Ganga and Jamuna
Now, substituting \( S \) back to find \( J \) and \( G \):
1. For Jamuna:
\[ J = 2S = 2 \times 3 = 6 \text{ days} \]
2. For Ganga:
\[ G = \frac{2S}{3} = \frac{2 \times 3}{3} = 2 \text{ days} \]

### Step 7: Calculate the Difference
Finally, we need to find the difference between the number of days taken by Ganga and Saraswati:
\[ \text{Difference} = S - G = 3 - 2 = 1 \text{ day} \]

### Conclusion
The difference between the number of days taken by Ganga and Saraswati is **1 day**.