A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 litres of petrol is used daily, the supply fails in 90 days. If 32,000 litres of petrol is used . daily, it fails in 60 days. How much petrol can be used daily without the supply ever failing?

Options

A. 64000 litres
B. 56000 litres
C. 8000 litres
D. 60000 litres

Answer

To solve the problem, we need to determine how much petrol can be used daily without the supply ever failing. We will set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( F \) = the daily filling rate of the reservoir (in liters)
- \( C \) = the total capacity of the reservoir (in liters)

### Step 2: Set Up Equations
From the problem, we have two scenarios:

1. When 40,000 liters are used daily, the supply lasts for 90 days:
\[ C - 40,000 \times 90 + F \times 90 = 0 \]
Rearranging gives us:
\[ C + 90F = 3,600,000 \quad \text{(Equation 1)} \]

2. When 32,000 liters are used daily, the supply lasts for 60 days:
\[ C - 32,000 \times 60 + F \times 60 = 0 \]
Rearranging gives us:
\[ C + 60F = 1,920,000 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we have two equations:
1. \( C + 90F = 3,600,000 \)
2. \( C + 60F = 1,920,000 \)

We can eliminate \( C \) by subtracting Equation 2 from Equation 1:
\[ (C + 90F) - (C + 60F) = 3,600,000 - 1,920,000 \]
This simplifies to:
\[ 30F = 1,680,000 \]
Now, divide both sides by 30:
\[ F = \frac{1,680,000}{30} = 56,000 \text{ liters} \]

### Step 4: Conclusion
Thus, the daily filling capacity \( F \) is 56,000 liters. This means that the maximum amount of petrol that can be used daily without the supply ever failing is **56,000 liters**.