Question

At t minutes past 5 pm, the time needed by the minutes hand of a clock to show 6 pm was found to be 12 minutes less than $\frac{t^2}{6}$ minutes. The value of t is

• A. 15
• B. 21
• C. 18
• D. 24

Answer 1

The correct option is C 18

Time travelled by the minute hand from t minutes past 5 pm to 6 pm is (60 – t) min.
$\therefore 60-t=\frac{t^2}{6}-12\left(Given\right)$
$\Rightarrow 360-6t=t^2-72$
$\Rightarrow t^2+6t-432=0$
$\Rightarrow t^2+24t-18t-432=0$
$\Rightarrow (t+24)(t-18)=0$
$\Rightarrow t=18ort=-24$
$\Rightarrow t=18min\text{Since, t cannot be negative}$
Hence, the correct answer is option (3).