Question

When a bucket is half full, the weight of the bucket and the water is $10\text{kg}$. When the bucket is two-thirds full, the total weight is $11\text{kg}$. What is the total weight, in kg, when the bucket is completely full?

• A. $12\text{kg}$
• B. $12\frac{1}{2}\text{kg}$
• C. $12\frac{2}{3}\text{kg}$
• D. $13\text{kg}$

Answer 1

The correct option is D $13\text{kg}$

Let the weight of the empty bucket be $B$ kg and total weight of water it can accommodate be $W$ kg.

$\therefore B+\frac{W}{2}=10...\left(1\right)$

Also, $B+\frac{2W}{3}=11...\left(2\right)$

Subtracting (1) from (2), we have

$\frac{2W}{3}-\frac{W}{2}=1$

$\therefore \frac{4W-3W}{6}=1$ or $W=6$

Substituting $W=6$ in (1)

$⟹B+\frac{6}{2}=10$

$\therefore B=7$

Total weight when completely filled $=B+W=13$ kg