# 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 t24 minutes. Find t. - Mathematics

Sum

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 t^2/4 minutes. Find t.

#### Solution

We know that, the time between 2 pm to 3 pm = 1 h = 60 min

Given that, at f min past 2 pm

The time needed by the min hand of a clock to show 3 pm was found to be 3 min less than t^2/4 min

i.e., t + (t^2/4 - 3) = 60

⇒ 4t + t^2 - 12 = 240

⇒ t^2 + 4t - 252 = 0

⇒ t^2 + 18t - 14t - 252 = 0   .....[By splitting the middle term]

⇒ t(t + 18) - 14(t + 18) = 0   ....[Since, time cannot be negative, so t ≠ - 18]

⇒ (t + 18)(t - 14) = 0

∴ t = 14 min

Hence, the required value off is 14 min.

Concept: Nature of Roots of a Quadratic Equation
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10