Question

When bucket is filled $\frac{3}{8}$ of its capacity its weight is $10kg$. If it is filled $\frac{3}{5}$ of its capacity its weight is $14.5kg$. How much will its weight be when it is filled to the full capacity?

• A. $20kg$
• B. $2.5kg$
• C. $22.5kg$
• D. $17.5kg$

Answer 1

Answer: (C)

$22.5kg$

Solution:

Let $x$ denotes capacity of bucket and $y$ denotes its weight

Let $x_1=\frac{3}{8}=0.375,y_1=10$

and $x_2=\frac{3}{5}=0.6,y_2=14.5$

Slope $m=\frac{y_2-y_1}{x_2-x_1}$

or, $m=\frac{14.5-10}{0.6-0.375}=20$

Point - slope form of straight line:

$y-y_1=m(x-x_1)$

or, $y-10=20(x-0.375)$

or, $y-10=20x-7.5$

or, $y=20x-7.5+10$

or, $y=20x+2.5$ is the equation.

Bucket is full when $x=1$

Put $x=1$ in above eqn. we get,

$y=20\times 1+2.5$

or, $y=22.5kg$

So, weight of the bucket when it is filled to the full capacity $=22.5kg$

Hence, C is the correct option.