Problem : At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t2/4 minutes. Find t.
Doubt by Muskan
Solutions :
t minutes past 2 pm = 2 O'clock + t minutes
3 pm = t minutes + [(t2/4) - 3 minutes]
Number of Minutes between 2 PM and 3 PM = 60 Minutes
ATQ
t + (t2/4) - 3 = 60
(4t + t2 - 12) / 3 = 60
4t + t2 - 12 = 240
t2 + 4t -12 - 240 = 0
t2 + 4t - 252 = 0
t2 + (18 - 14) t - 252 = 0
t2 + 18t - 14t - 252 = 0
t(t + 18) - 14 (t + 18) = 0
(t - 14) (t + 18) = 0
t - 14 = 0 OR t + 18 = 0
t = 14 OR t = - 18
t ≠ - 18 [ ∵ time can't be -ve ]
∴ t = 14