6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a USHA pump?

Options

A. `6:7`
B. `7:6`
C. `7:54`
D. can't be determined

Answer

To solve the problem, we need to find the ratio of the efficiency of Kirloskar pumps to USHA pumps based on the information provided.

### Step-by-Step Solution:

1. **Determine the filling capacity of Kirloskar pumps:**
- Given that 6 Kirloskar pumps can fill a tank in 7 days, we first find out how long it takes for 1 Kirloskar pump to fill the tank.
- Total work done (in terms of tank filling) by 6 pumps in 7 days = 1 tank.
- Therefore, work done by 1 pump in 7 days = 1/6 tank.
- Work done by 1 Kirloskar pump in 1 day = (1/6) / 7 = 1/42 tank.

2. **Determine the filling capacity of USHA pumps:**
- Given that 2 USHA pumps can fill the same tank in 18 days, we find out how long it takes for 1 USHA pump to fill the tank.
- Total work done by 2 pumps in 18 days = 1 tank.
- Therefore, work done by 1 pump in 18 days = 1/2 tank.
- Work done by 1 USHA pump in 1 day = (1/2) / 18 = 1/36 tank.

3. **Calculate the efficiency of each pump:**
- Efficiency of a pump is inversely proportional to the time taken to fill the tank.
- Efficiency of 1 Kirloskar pump (EK) = 1 / (Time taken by 1 Kirloskar pump) = 1 / (42 days) = 1/42.
- Efficiency of 1 USHA pump (EU) = 1 / (Time taken by 1 USHA pump) = 1 / (36 days) = 1/36.

4. **Find the ratio of the efficiencies:**
- The ratio of the efficiency of Kirloskar pump to USHA pump is given by:
\[ \text{Ratio} = \frac{EK}{EU} = \frac{1/42}{1/36} = \frac{36}{42} = \frac{6}{7}. \]

### Final Answer:
The ratio of the efficiency of a Kirloskar pump to a USHA pump is **6:7**.

---