A bucket of 16 litres capacity is filled to the brim with water. Water from this bucket is to be transferred into smaller utensils. A mug filled to capacity has to be dipped 50 times to completely transfer the water in the bucket into the utensils. What is the capacity of the mug ?

Question

Accepted Answer

To determine the capacity of the mug, we need to understand how the total volume of water in the bucket is distributed across the number of times the mug is dipped into it. The bucket has a total capacity of 16 liters, which is equivalent to 16,000 milliliters (since 1 liter = 1,000 milliliters).

Given that the mug is dipped 50 times to completely transfer the water from the bucket, we can calculate the capacity of the mug by dividing the total volume of water by the number of dips:

$$ \text{Capacity of the mug} = \frac{\text{Total volume of water in the bucket}}{\text{Number of dips}} $$

$$ \text{Capacity of the mug} = \frac{16,000 \text{ mL}}{50} $$

$$ \text{Capacity of the mug} = 320 \text{ mL} $$

Therefore, the capacity of the mug is 320 milliliters, which corresponds to Option 4.

Now, let's explain why each of the other options is incorrect:

1. **Option 1: 225 mL**  
   If the mug had a capacity of 225 mL, then the total volume transferred by 50 dips would be:  
   $$ 225 \text{ mL} \times 50 = 11,250 \text{ mL} $$  
   This is significantly less than the total volume of 16,000 mL in the bucket, so this option is incorrect.

2. **Option 2: 250 mL**  
   If the mug had a capacity of 250 mL, then the total volume transferred by 50 dips would be:  
   $$ 250 \text{ mL} \times 50 = 12,500 \text{ mL} $$  
   This is also less than the total volume of 16,000 mL in the bucket, making this option incorrect.

3. **Option 3: 275 mL**  
   If the mug had a capacity of 275 mL, then the total volume transferred by 50 dips would be:  
   $$ 275 \text{ mL} \times 50 = 13,750 \text{ mL} $$  
   This is still less than the total volume of 16,000 mL in the bucket, so this option is incorrect.

In conclusion, only Option 4, with a capacity of 320 mL, correctly accounts for the total volume of water in the bucket when the mug is dipped 50 times.