Question

At t minutes past 2 p.m. , the time needed by the minutes hands of a clock to show 3 p.m. was found to be 3 minutes less than t.Find t ?.

• A. $14$
• B. $30$
• C. $36$
• D. $40$

Answer 1

Answer: (A)

$14$

Given time needed by minute hand $=\frac{t^2}{4}=3$

Here quadratic equation becomes $\frac{t^2}{4}-3=60$

$\frac{t^2-12}{4}=60-t\Rightarrow t^2-12=4(60-t)\Rightarrow t^2-12=240-4t\Rightarrow t^2+4t-12-240=0\Rightarrow t^2+4t-252=0\Rightarrow t^2+18t-14t-252=0\Rightarrow t(t+18)-14(t+18)=0(t+18)(t-14)=0$
So either $(t+18)=0or(t-14)=0$

$\therefore t=14$ and not $-18$on it cannot be negative.