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10 Jan 2020, 02:59
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Difficulty:
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Question Stats:
73% (01:50) correct
27%
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If A, B and C take 12 mins, 15 mins and 20 mins to complete one full round of a circular track, after how much time will all three A, B and C meet for the first time, if they start from the same point at the same time, with A and C running in clockwise direction and B running in anti-clockwise direction?
A. 1/2 hours
B. 1 hour
C. 2 hours
D. 5 hours
E. 30 hours
Are You Up For the Challenge: 700 Level Questions
A. 1/2 hours
B. 1 hour
C. 2 hours
D. 5 hours
E. 30 hours
Are You Up For the Challenge: 700 Level Questions
10 Jan 2020, 03:55
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Asume length of track= LCM(12,15,20)= 60.
speed of A= 5m/min
speed of B= 4m/min
speed of C= 3m/min
Time taken by A and C to meet=\( \frac{60}{(5-3)}\)= 30min ( Both are running in same direction)
Time taken by A and B to meet= \(\frac{60}{(5+4)}= \frac{60}{9}\) min ( Both are running in opposite direction)
Time taken by B and C to meet=\( \frac{60}{(4+3)}= \frac{60}{7}\) min ( Both are running in opposite direction)
time after which all three A, B and C meet for the first time= LCM(30, 60/9,60/7)= \(\frac{LCM(30,60,60)}{HCF(1,9,7)}\)= 60mins
speed of A= 5m/min
speed of B= 4m/min
speed of C= 3m/min
Time taken by A and C to meet=\( \frac{60}{(5-3)}\)= 30min ( Both are running in same direction)
Time taken by A and B to meet= \(\frac{60}{(5+4)}= \frac{60}{9}\) min ( Both are running in opposite direction)
Time taken by B and C to meet=\( \frac{60}{(4+3)}= \frac{60}{7}\) min ( Both are running in opposite direction)
time after which all three A, B and C meet for the first time= LCM(30, 60/9,60/7)= \(\frac{LCM(30,60,60)}{HCF(1,9,7)}\)= 60mins
Bunuel
General Discussion
10 Jan 2020, 03:11
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Bunuel
Bunuel Please check the units of the given options,
assuming
A. 1/2 hour
B. 1 hour
C. 2 hour
Substitute the options and check
Number of rounds made by A, B & C after 't' mins = t/12, t/15 & t/20 respectively
No. of rounds -------- A ----- B ----- C
Time (mins)
-- 30 ----------------- 2.5 --- 2 ---- 1.5 --> No
-- 60 ----------------- 5 ----- 4 ----- 3 --> Yes [Everyone met at the starting point for the first time]
IMO Option B
