10 engines consume 80 litres diesel when each is running 9 hours a day. How much diesel will be required for 10 engines, each running 15 hours a day, whereas 6 engines of the former type consume as much as 5 engines of latter type?

Options

A. 160 litre
B. 75 litre
C. 80 litre
D. `111 1/9` litre

Answer

To solve the problem step by step, we need to analyze the information given and calculate the diesel consumption for both types of engines.

### Step 1: Calculate the diesel consumption for one Type A engine.
We know that 10 Type A engines consume 80 liters of diesel when each is running for 9 hours a day.

\[ \text{Diesel consumption for 1 Type A engine} = \frac{80 \text{ liters}}{10} = 8 \text{ liters} \]

### Step 2: Calculate the hourly consumption for one Type A engine.
Since each Type A engine runs for 9 hours a day, we can find out how much diesel one Type A engine consumes per hour.

\[ \text{Hourly consumption for 1 Type A engine} = \frac{8 \text{ liters}}{9 \text{ hours}} = \frac{8}{9} \text{ liters/hour} \]

### Step 3: Calculate the diesel consumption for 6 Type A engines.
Now, we need to find out how much diesel 6 Type A engines consume per hour.

\[ \text{Consumption for 6 Type A engines} = 6 \times \frac{8}{9} = \frac{48}{9} = \frac{16}{3} \text{ liters/hour} \]

### Step 4: Establish the relationship with Type B engines.
According to the problem, the consumption of 5 Type B engines is equal to the consumption of 6 Type A engines. Therefore, we can set up the equation:

\[ \text{Consumption of 5 Type B engines} = \frac{16}{3} \text{ liters/hour} \]

### Step 5: Calculate the hourly consumption for one Type B engine.
To find out the consumption for one Type B engine, we divide the total consumption of 5 Type B engines by 5.

\[ \text{Hourly consumption for 1 Type B engine} = \frac{\frac{16}{3}}{5} = \frac{16}{15} \text{ liters/hour} \]

### Step 6: Calculate the diesel consumption for 10 Type B engines.
Now, we need to find out the consumption for 10 Type B engines.

\[ \text{Consumption for 10 Type B engines} = 10 \times \frac{16}{15} = \frac{160}{15} = \frac{32}{3} \text{ liters/hour} \]

### Step 7: Calculate the total consumption for 10 Type B engines running for 15 hours.
Finally, we need to calculate how much diesel 10 Type B engines will consume when they run for 15 hours a day.

\[ \text{Total consumption for 10 Type B engines in 15 hours} = \frac{32}{3} \times 15 = \frac{480}{3} = 160 \text{ liters} \]

### Final Answer:
The total diesel required for 10 engines of Type B, each running 15 hours a day, is **160 liters**.

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