New Questions to solve.?

[assignus]

Originally Posted by DesiGuru

I dont get the need for this complication
She went out at 4:25 and came back at 5:20
Isnt the above correct too?

K

lol.....understand that at 4:25 the hour hand is not exactly at 4 (but midway between 4 & 5) ...same applies to 5:20 where the hour hand is not exactly at 5....

thats why the above complication.... ....now figure out...

[khanna_sumit]

Originally Posted by assignus

its easy to deduce that time at which xyz leaves is between 4:25-4:30
and time when xyz returns is 5:20-5:25

now...Hours hand moves 5 degrees in 60 min..
say left time is 4:X minutes...... so in X min Hours hand moves (5xX)/60 degrees

Now returm time in terms of X is 5 hours [20+(5xX)/60] minutes

now calculate how many degrees hours hand moves in [20+(5xX)/60] minutes .....this added to 25 minutes will the position of hours hand when xyz returns...... that is also equal to X ..i.e

X=25+(5/60) [20+(5xX)/60]

solving u get X=26.8531 = 26 min 51.18 sec

hope it helps..

ps: is there any shortcut..or a simpler way of solving?

we know the speeds of minute's and hour's hand........if we divide the clock into 12 units then speed of minute's hand is 12 units/hr and that of hours hand is 1 unit/hr....if persons remains out of his house for x hours then distance covered by the two hands is = 12*x and 1*x respectively....and since these interchange the positions then by little reasoning we will understand that total distance covered by the two hands collectively should be 12 units....hence 12x+x=12
and x=12/13 hrs.....therefore person remains out of his house for 12/13 hrs....

[DesiGuru]

Originally Posted by assignus

lol.....understand that at 4:25 the hour hand is not exactly at 4 (but midway between 4 & 5) ...same applies to 5:20 where the hour hand is not exactly at 5....

thats why the above complication.... ....now figure out...

got it... Ur right...

K

[sbhaskaran2k]

ya he is right it is not 5:20 and 4:25

[jockey]

desiguru, at 4:25 ur min hand is exactly at 25 min but at 5:20 hour hand is not exactly at 25 min as it has moved 10 degree bcoz hour hand moved 1/2 degree in a min, hope it's clear and non mathematical explanation.

as far as short cut is concerned, lemme try

had the question been , for how many min. she is out of the house, the answer would have been.......

if they are interchanging their position that means together they have cover 360 degrees. as hour hand has taken min hands position and vice- versa. min hand moves 6 deg and hour hand moves 1/2 deg in a min, together they move 13/2 deg in a min.

in 1 min they are moving 13/2 deg

so together 1 deg they will be moving in 2/13 min

so 360 deg in 360 x 2/13 min i.e 720/13 min

that means she remain 720/13 min out fo her place

this much is easy, and i think one can do it in 10 sec.

but question is diff, we have have to find what is the time

ratio of speed of min and hour hand is 12:1

that means hour hand has moved 1/13 part of 720/13 i.e 720/169 min, converting it into deg it's 720/169 x 6 = 4320/169 deg, now the logic starts, by travelling 4320/169 deg hour hand reaches at the position of min hand that mean intially min hand is 4320/169 deg ahead of hour hand.

at 4:00 min hand is 120 deg behind hour hand, as we know their relative speed we can easily find when will they meet i.e when min hand will cover 120 deg more than hour hand

in 1 min min hand cover 11/2 deg more than hour hand ( their relative speed )
1 deg in 2/11 min

so 120 deg in 240/11 min


in this question min hand has to cover 120 + 4320/160 =24600/169 deg more than hour hand

so time taken is 24600/169 x 2/11 = 26.46 min

that mean actuall time is 4 hrs 26.46 min

i know the silution is verbose but if u understand the logic u can call it a shortcut, there would be many ppl who will not take it as a shortcut, for them all i can say is then take it as an alternative way of solving the question

wat do u say assignus and bhaskaran

[EuPhOrIa]

assignus has a better soln. Logic is bang on target n simpler one once understood...if the logic is understood that an hour hand moves 1/12 position every hour, guess we'd be able to solve clock probs quite easily.

Congo!!

[Eccentric]

Originally Posted by sbhaskaran2k

1) Padmaja left her residence between 4 and 5 'o clock and returned back between 5 and
6 'o clock . She notices that the hour hand and minute hand of the clock interchanged
theie position with what they were when she went out. Wht time did she go out and when
diod she return ?
Help me to solve these questions?

If you just need the out time:
Speed of hour hand = 360/60*12 =1/2deg per min
Speed of min hand = 6deg per min.

Lets say originally the angle was x deg between min and Hour hand (where min hand is ahead of hour hand)

As both hand replace position in the Next T min,
angle moved by hour hand = x deg , Time = x/(1/2) = 2x
angle moved by min hand = (360-x) deg, time= (360-x)/6
these times are qual

2x = (360-X)/6
x=360/13 deg
time taken = 2x min (as specified above for hour hand) = 720/13 min



Had he gone between 3 and 4 and come bak between 5 and 6
2x = (720-x) //720-x because min hand has taken one complete turn + 360-x turn!
x=720/13
time taken = 1440/13 min

[khanna_sumit]

Originally Posted by EuPhOrIa

assignus has a better soln. Logic is bang on target n simpler one once understood...if the logic is understood that an hour hand moves 1/12 position every hour, guess we'd be able to solve clock probs quite easily.

Congo!!

thanx for the appericiation euphoria but this solution was given by me SUMIT and not assignus

[sbhaskaran2k]

1) Padmaja left her residence between 4 and 5 'o clock and returned back between 5 and
6 'o clock . She notices that the hour hand and minute hand of the clock interchanged
theie position with what they were when she went out. Wht time did she go out and when
diod she return ?

Hi guys ,

the above question is taken from time material and the answers they had given is


she left at 4 hrs 26 min 122/143 secs ( 4 26 122/143 )

and shed returned back at 5 hrs 22min 34/143 secs ( 5 22 34/143 )


can anyone able to arrive at this solution ??

[assignus]

Originally Posted by sbhaskaran2k

1) Padmaja left her residence between 4 and 5 'o clock and returned back between 5 and
6 'o clock . She notices that the hour hand and minute hand of the clock interchanged
theie position with what they were when she went out. Wht time did she go out and when
diod she return ?

Hi guys ,

the above question is taken from time material and the answers they had given is


she left at 4 hrs 26 min 122/143 secs ( 4 26 122/143 )

and shed returned back at 5 hrs 22min 34/143 secs ( 5 22 34/143 )


can anyone able to arrive at this solution ??

hi bhaskaran.....i guess couple of ppl (inc me) have posted solutions to the above prob... refer them..