At t minutes past 2 pm, the time needed by the minute hand of a clock to show 3 pm was found to be 3 minutes less than t²/4 minutes. Find t

Solution:

Given, at t minutes past 2 pm time needed by the minute hand to show 3pm was 3 minutes less than t²/4 minutes.

We have to find the value of t.

Time taken by the minute hand to travel from 2 pm to 3 pm = 60 minutes

So, t minutes past 2, the time needed to show 3 is 60-t.

As per given condition,

60 - t = (t²/4 - 3)

60 - t = (t² - 12)/4

240 - 4t = t² - 12

t² + 4t - 12 - 240 = 0

t² + 4t - 252 = 0

On factoring,

t² - 14t + 18t - 252 = 0

t(t - 14) + 18(t - 14) = 0

(t + 18)(t - 14) = 0

Now, t - 14 = 0

t = 14

Also, t + 18 = 0

t = -18

Since time cannot be negative, t = -18 is neglected.

Therefore, the value of time t is 14 minutes.

✦ Try This: At t minutes past 4 pm, the time needed by the minute hand of a clock to show 5 pm was found to be 3 minutes less than t²/4 minutes. Find t

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

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NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 8

At t minutes past 2 pm, the time needed by the minute hand of a clock to show 3 pm was found to be 3 minutes less than t²/4 minutes. Find t

Summary:

At t minutes past 2 pm, the time needed by the minute hand of a clock to show 3 pm was found to be 3 minutes less than t²/4 minutes, then t is 14 minutes

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