13 barrels of wine fill a tank when the capacity of each barrel is 51 litres . How many barrels will be needed to fill the same tank , if the capacity of each barrel is 17 litres ?

Options

A. 39
B. 37
C. 91
D. 42

Answer

To solve the problem step by step, we will first determine the total capacity of the tank using the information given about the barrels and then find out how many smaller barrels are needed to fill the same tank.

### Step 1: Calculate the total capacity of the tank
We know that 13 barrels of wine fill the tank and each barrel has a capacity of 51 litres.

\[ \text{Total capacity of the tank} = \text{Number of barrels} \times \text{Capacity of each barrel} \]
\[ \text{Total capacity of the tank} = 13 \times 51 \]
\[ \text{Total capacity of the tank} = 663 \text{ litres} \]

### Step 2: Determine how many barrels of 17 litres are needed
Now, we need to find out how many barrels of 17 litres are required to fill the same tank.

Let \( n \) be the number of barrels needed.

\[ n \times \text{Capacity of each smaller barrel} = \text{Total capacity of the tank} \]
\[ n \times 17 = 663 \]

### Step 3: Solve for \( n \)
To find \( n \), we will divide the total capacity of the tank by the capacity of each smaller barrel.

\[ n = \frac{663}{17} \]

Calculating the division:

\[ n = 39 \]

### Conclusion
Therefore, **39 barrels** of 17 litres each will be needed to fill the tank.

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