Question

Satvik observed that in a clock, the time needed by the minute hand of a clock to show 3 PM was found to be 3 min less than `"t"^2/4` minutes at t minutes past 2 PM. Then t is equal to:

Options

• 14

• 15

• 16

• None of these

Answer 1

14

Explanation:

We know that the time between 2 PM to 3 PM = 1 hr = 60 min

Given that at t minutes past 2 PM, the time needed by the minute’s hand of a clock to show 3 PM was found to be 3 minutes less than `"t"^2/4` minutes.

Therefore,

`"t" + ("t"^2/4 - 3)` = 60

4t + t² − 12 = 240

t² + 4t − 252 = 0

t² + 18t − 14t − 252 = 0

(t + 18) (t − 14) = 0

t = 14 min