When a bucket is half full,the weight of the | vedclass

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(D) Let the weight of the empty bucket be $x \ kg$ and the weight of the water when the bucket is completely full be $y \ kg$.According to the problem

Vedclass · Accepted Answer

$13$

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(D) Let the weight of the empty bucket be $x \ kg$ and the weight of the water when the bucket is completely full be $y \ kg$.According to the problem:$x + \frac{y}{2} = 10$  $(i)$$x + \frac{2y}{3} = 11$  $(ii)$Subtracting equation $(i)$ from equation $(ii)$:$(x + \frac{2y}{3}) - (x + \frac{y}{2}) = 11 - 10$$\frac{2y}{3} - \frac{y}{2} = 1$$\frac{4y - 3y}{6} = 1$$\frac{y}{6} = 1 \implies y = 6 \ kg$Substituting $y = 6$ in equation $(i)$:$x + \frac{6}{2} = 10$$x + 3 = 10 \implies x = 7 \ kg$The total weight when the bucket is completely full is $x + y = 7 + 6 = 13 \ kg$.

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

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