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# If A, B and C take 12 mins, 15 mins and 20 mins to complete one full

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Math Expert
Joined: 02 Sep 2009
Posts: 61544
If A, B and C take 12 mins, 15 mins and 20 mins to complete one full  [#permalink]

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10 Jan 2020, 01:59
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:57) correct 22% (02:00) wrong based on 18 sessions

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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

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VP
Joined: 20 Jul 2017
Posts: 1337
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If A, B and C take 12 mins, 15 mins and 20 mins to complete one full  [#permalink]

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10 Jan 2020, 02:11
Bunuel wrote:
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 minutes
B. 1 minute
C. 2 minutes
D. 5 minutes
E. 30 minutes

Are You Up For the Challenge: 700 Level Questions

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
VP
Joined: 19 Oct 2018
Posts: 1314
Location: India
Re: If A, B and C take 12 mins, 15 mins and 20 mins to complete one full  [#permalink]

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10 Jan 2020, 02:55
1
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

Bunuel wrote:
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
Re: If A, B and C take 12 mins, 15 mins and 20 mins to complete one full   [#permalink] 10 Jan 2020, 02:55
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