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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 $\frac{t^{2}}{4}$ minutes. What is the value of $t$ ?

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13

12

14

15

answer is C.

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Detailed Solution

It is given that at

t

minutes past

2

pm, the time needed by the minute's hand to show

3

pm is

3

minutes less than

\frac{t^{2}}{4}

minutes
According to the given condition,

(60 − t) = t 2 4 − 3 ⇒ 60 − t = t 2 − 12 4 ⇒ 240 − 4 t = t 2 − 12 ⇒ t 2 + 4 t − 252 = 0

Now, factorize the equation.

⇒ t 2 + 18 t − 14 t − 252 = 0 ⇒ t (t + 18) − 14 (t + 18) = 0 ⇒ (t − 14) (t + 18) = 0 ⇒ t = 14, − 18

t = − 18

is neglected because time cannot be negative.
So, the value of

t is 14

.
Hence, the correct option is 3.

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