Question

The robot's battery usage rate is $\frac{7}{2}\%$ per mile. The robot's battery recharges by $\frac{22}{3}\%$ at points A and B.


A fully charged robot starts its journey from base to A, then go to B, and returns back to the base. What is the power status of the robot after returning to its base?

• A. 44%
• B. 49%
• C. 61%
• D. 63%

Answer 1

The correct option is C 61%

Power usage of the robot from base to A = $\frac{7}{2}$ x 5%

Power usage of the robot from A to B
= $\frac{7}{2}$ x $\frac{4}{3}$%

Power usage of the robot from B to base = $\frac{7}{2}$ x 9%

Recharge rate = $\frac{22}{3}$ %

Final power status

= 100 + (-$\frac{7}{2}$ x 5) + $\frac{22}{3}$ + (-$\frac{7}{2}$ x $\frac{4}{3}$) + $\frac{22}{3}$ + (-$\frac{7}{2}$ x 9)

= 100 + (-$\frac{35}{2}$) + $\frac{22}{3}$ + (-$\frac{28}{6}$) + $\frac{22}{3}$+ (-$\frac{63}{2}$)

= 100 + {(-$\frac{35}{2}$) + (-$\frac{63}{2}$)} + {$\frac{22}{3}$ + (-$\frac{28}{6}$) +$\frac{22}{3}$} [by associative property]

= 100 - ($\frac{98}{2}$) + ($\frac{44}{3}$ - $\frac{28}{6}$)

= 100 - 49 + $\frac{60}{6}$

= 100 + 10 - 49 [by commutative property]

= 61

Hence, the power status of the robot after returning to base is 61%.