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. 0.25486111111111
B. 0.29583333333333
C. 0.32916666666667
D. can't be determined

Answer

To find the ratio of the efficiency of a Kirlosker pump to a USHA pump, we can follow these steps:

### Step 1: Calculate the total work done by each type of pump
- For Kirlosker pumps:
- 6 pumps can fill the tank in 7 days.
- Total work done by 6 Kirlosker pumps in 7 days = 6 pumps × 7 days = 42 pump-days.

- For USHA pumps:
- 2 pumps can fill the tank in 18 days.
- Total work done by 2 USHA pumps in 18 days = 2 pumps × 18 days = 36 pump-days.

### Step 2: Determine the work done by one pump of each type
- Work done by one Kirlosker pump in one day:
- Total work = 42 pump-days, so work done by one Kirlosker pump = 42 pump-days / 6 pumps = 7 pump-days per pump.

- Work done by one USHA pump in one day:
- Total work = 36 pump-days, so work done by one USHA pump = 36 pump-days / 2 pumps = 18 pump-days per pump.

### Step 3: Calculate the efficiency of each pump
- Efficiency of a Kirlosker pump = 1/7 (since it takes 7 days to fill the tank).
- Efficiency of a USHA pump = 1/18 (since it takes 18 days to fill the tank).

### Step 4: Find the ratio of the efficiencies
- Ratio of efficiency of Kirlosker pump to USHA pump:
- Efficiency (Kirlosker) : Efficiency (USHA) = (1/7) : (1/18)
- To find the ratio, we can cross-multiply:
- (1/7) ÷ (1/18) = 18/7.

Thus, the ratio of the efficiency of a Kirlosker pump to a USHA pump is 18:7.

### Final Answer:
The ratio of the efficiency of a Kirlosker pump to a USHA pump is **18:7**.

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