The Clock Tower.

Geometry Level 2

My mother prepares lunch for my school.She. usually finishes cooking it 20 to 30 minutes before my school bus arrives.My school starts from 8:15 a.m. One fine morning,she was staccidentally veggies under the sandwich bread when her eyes fell on the giant clock tower situated in our colony. From the look on her face,I could tell that she must have noticed something interesting over there.The next moment,I saw her yelling with pain.She had burnt her index finger by accid shoving her hand into the stove flames.I heard the scream and came running to her. ''Mom,what were you looking at?'',I inquired. She answered to me,''Oh dear!,the time on the clock was such that the minute hand and the hour hand were perfectly lying on each other.Isn't that amazing?''. If the time on the clock when my mother had that unfortunate burn was H:M a.m.,then find the value of H+M.

The answer is 45.

2 solutions

Mohd Faraz
Jan 27, 2017

Can you tell how many times a day second, minute and hour hand coincides?

Rishi Hazra
Nov 6, 2014

Judging form the question stating that the mother was cooking at that very moment, we can say that the time must have been 7 past something. That means the hour's hand has traversed 210 degrees + something.

Now for every 1 degree of movement for the minute's hand results in 1/ 12 degrees of movement for the hour's hand.

Let the minute hand traverse ' x ' degrees at that very moment.

for ' x ' degree of traversal of the minute' hand, the hour's hand must have moved by ' x / 12 ' degrees.

Total angle traversed by minute's hand = total angle traversed by the hour's hand

=> x = 210 + x/12

solving the equation gives us x = 229 degrees

that means the time is 7:38

The Clock Tower.

The answer is 45.

2 solutions

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