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 frac 1\9` litre

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the diesel consumption per engine per hour for the first type of engine.
Given that 10 engines consume 80 liters of diesel when each is running for 9 hours a day, we can first calculate the total hours for all engines combined.

Total hours for 10 engines = 10 engines × 9 hours = 90 hours.

Now, we can find the diesel consumption per hour for all engines:
Diesel consumption per hour for 10 engines = Total diesel / Total hours
= 80 liters / 90 hours
= 8/9 liters per hour for 10 engines.

Now, to find the consumption per engine per hour:
Diesel consumption per engine per hour = (8/9 liters) / 10 engines
= 8/90 liters
= 4/45 liters per engine per hour.

### Step 2: Calculate the diesel consumption for 10 engines running 15 hours a day.
Now, we need to find out how much diesel will be required for 10 engines running for 15 hours a day.

Total hours for 10 engines = 10 engines × 15 hours = 150 hours.

Now, we calculate the total diesel consumption for these 10 engines:
Diesel consumption for 10 engines = Diesel consumption per engine per hour × Total hours
= (4/45 liters per hour) × 150 hours
= (4 × 150) / 45 liters
= 600 / 45 liters
= 40/3 liters.

### Step 3: Determine the relationship between the two types of engines.
According to the problem, 6 engines of the first type consume as much as 5 engines of the second type. This means we need to find the consumption of the second type of engine.

Let the diesel consumption per engine per hour for the second type be x liters.

From the relationship given:
6 engines of the first type = 5 engines of the second type.

So, we can set up the equation:
6 × (4/45) × 9 = 5 × x × 15.

Calculating the left side:
6 × (4/45) × 9 = (24/45) × 9 = 216/45 liters.

Now, we can set up the equation:
216/45 = 5 × x × 15.

### Step 4: Solve for x.
Now we can solve for x:
x = (216/45) / (5 × 15)
= (216/45) / 75
= 216 / (45 × 75)
= 216 / 3375.

### Step 5: Calculate the total diesel required for the second type of engine.
Now, we need to find out how much diesel will be required for 10 engines of the second type running for 15 hours a day.

Total diesel consumption for 10 engines of the second type:
= 10 × x × 15
= 10 × (216/3375) × 15
= (10 × 216 × 15) / 3375
= 21600 / 3375
= 6.4 liters.

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

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