Question

The robot's battery usage rate is 7/2% per km. The robot's battery recharges by 22/3% at points A and B.

The robot starts it journey from base to A, then to B, and returns back to the base. What is the power status of the robot after returning to 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

Therefore, option (c) is the correct answer.