Question

The given table and the graph shows the amount of work done by workers P, Q, and R and the time taken. Which of the following workers shows a proportional relationship?

P
x: Time (in days)	$\frac{12}{15}$	$\frac{5}{2}$
y: Amount of work done	$\frac{1}{3}$	$\frac{2}{3}$

• A. R and Q
  
• B. P, Q, and R
  
• C. R
• D. P

Answer 1

The correct option is A R and Q


$P:\frac{y}{x}=\frac{1}{3}÷\frac{12}{15}=\frac{1}{3}\times \frac{15}{12}=\frac{5}{12}$

$\frac{y}{x}=\frac{2}{3}÷\frac{5}{2}=\frac{2}{3}\times \frac{2}{5}=\frac{4}{15}$
Hence, the amount of work done by P is not in a proportional relationship with time.
The graphs of both R and Q are straight lines and pass through the origin.
Thus, the graphs of R and Q show a proportional relationship.