ISI Maths

Question

The hands of a clock are observed continuously from 12:45 p.m. onwards. They will be observed to point in the same direction some time between
(A) 1:03 p.m. and 1:04 p.m. ;                (B) 1:04 p.m. and 1:05 p.m. ;
(C) 1:05 p.m. and 1:06 p.m. ;                (D) 1:06 p.m. and 1:07 p.m.

Answer 1

At 12:45, the minute hand is on the 9 ( 90° between 9 and 12) and the hour hand is 3/4 of the way between 12 and 1

so the degree value from 12 to 1 is:. There are 30° between numbers, so it is=(3/4*30)= 22½° past 12

Every minute, the minute hand goes 6° while the hour hand goes ½° so it is gaining on it by 5½° per minute. 

so after 15 minute the minute + (3/4) of 5 minute it will coincide with hour hand  travelling  a degree of   112½° 

It has to make up 112½° so dividing by 5½°/minute we have: 
112.5 / 5.5 
= 20.45 

Adding to 12:45, we get a time between 1:05 and 1:06. 

Answer: 
c) 1:05 pm and 1:06 pm

Answer 2

one of the method to solve such problems is 

hours H : M minutes

30H:11/2 M

3o(12):11/2(45)

360-247.5=112.5 degrees

in the options hours hand is in 1

then  we have to find miutes

30(1):11/2(M)

60:11M

m=60/11

M=5.45 so it is between 5 and 6

we get time between  1.05 pm and 1.06 pm

so the ans is (c)