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10 Dec 2021, 03:15
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Difficulty:
75%
(hard)
Question Stats:
59% (02:25) correct
41%
(02:43)
wrong
based on 143
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Modi and Shah started simultaneously in opposite directions from towns A and B respectively. Each of them run towards starting point of other. After crossing each other Modi and Shah took 40 minutes and 90 minutes respectively to reach their destinations. Find the time taken (in minutes) by them to meet each other.
A) 50
B) 60
C) 72
D) 80
E) 100
Are You Up For the Challenge: 700 Level Questions
A) 50
B) 60
C) 72
D) 80
E) 100
Are You Up For the Challenge: 700 Level Questions
10 Dec 2021, 03:55
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\(\frac{S_1}{S_2} = \sqrt{\frac{t_2}{t_1}}\)
ie. \(\frac{S_m}{S_s} = \sqrt{\frac{t_s}{t_m}}\)
ie. \(\frac{S_m}{S_s} = \sqrt{\frac{90}{40}} = \frac{3}{2}\)
i.e. Total Distance = 40*3 + 90*2 = 300 (Assuming that speeds are 3 and 2 m/min)
Relative Speed = 3+2 = 5
Time to cross = 300/5 = 60 minutes
ANswer: Option B
12 Dec 2021, 00:57
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In this kind of problem the following short-cut is very useful:
t^2=60*40 (where t is the time taken to meet). T/4, t=60. ANS:B
This short-cut is derived from the fact that the ratio of the speeds of two moving objects is the inverse of the ratio of the times taken by each to cover the same distance.
A_______________M_______B (where M is the meeting point).
Let SM and SS be the speeds of Modi and Shah respectively. Then:
SM/SS=t/90....(i)
SS/SM=t/40....(ii)
Multiplying (i) and (ii), we get:
1=t^2/90*40...> t^2=90*40
t^2=60*40 (where t is the time taken to meet). T/4, t=60. ANS:B
This short-cut is derived from the fact that the ratio of the speeds of two moving objects is the inverse of the ratio of the times taken by each to cover the same distance.
A_______________M_______B (where M is the meeting point).
Let SM and SS be the speeds of Modi and Shah respectively. Then:
SM/SS=t/90....(i)
SS/SM=t/40....(ii)
Multiplying (i) and (ii), we get:
1=t^2/90*40...> t^2=90*40
