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13 Jun 2019, 23:53
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
75% (02:39) correct
25%
(02:44)
wrong
based on 356
sessions
History
Date
Time
Result
Not Attempted Yet
Xavier starts from P towards Q at a speed of 30 kilometre per hour and after every 12 minutes increases his speed by 5 kilometre per hour. If the distance between P and Q is 51 kilometres, then how much time does he take to cover the distance?
A. 60 minutes
B. 72 minutes
C. 90 minutes
D. 120 minutes
E. 100 minutes
A. 60 minutes
B. 72 minutes
C. 90 minutes
D. 120 minutes
E. 100 minutes
Updated on: 03 Jul 2024, 09:52
Originally posted by CareerGeek on 14 Jun 2019, 00:07.
Last edited by CareerGeek on 03 Jul 2024, 09:52, edited 1 time in total.
Last edited by CareerGeek on 03 Jul 2024, 09:52, edited 1 time in total.
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Bunuel
Every 12 minutes --> 12/60 = 1/5 hour Speed increases by 5 kmph
0 - 12 min, speed = 30 kmph, Distance covered = 30*1/5 = 6 miles
12 - 24 min, speed = 35 kmph, Distance covered = 35*1/5 = 7 miles
24 - 36 min, speed = 40 kmph, Distance covered = 40*1/5 = 8 miles
36 - 48 min, speed = 45 kmph, Distance covered = 45*1/5 = 9 miles
48 - 60 min, speed = 50 kmph, Distance covered = 50*1/5 = 10 miles
60 - 72 min, speed = 55 kmph, Distance covered = 55*1/5 = 11 miles
Total distance covered = 51 kms after 72 min
Alternate Method:
Distance covered in every 12 minutes will be in AP series, whose sum should be 51 miles
6, 7, 8, . . . .
--> 51 = n*(a + \(a_n\))/2 = n/2*(a + a + (n - 1)d)
--> 51 = n/2*(2*6 + (n - 1)1)
--> 102 = 12n + n^2 - n
--> n^2 + 11n - 102 = 0
--> (n + 17)(n - 6) = 0
--> n = 6
So total time = 6*12 = 72 min
IMO Option B
Pls Hit Kudos if you like the solution
General Discussion
Archit3110
Major Poster
14 Jun 2019, 01:51
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Bunuel
seems to be more like CAT not GMAT kinda question
initial speed = 30kmph
and increment is of 5kmph every 12 mins
so we can say 12/60 = 1/5 hr speed is increasing by 5 kmph
0-12 mins ; 30*1/5 = 6 km
12-24; 35*1/5= 7km
24-36; 40*1/5 = 8km
36-48; 45*1/5 ; 9 km
58-60 mins; 50*1/5 = 10 km
60-72 mins ; 55*1/5 = 11 km
total 56 km covered under 72mins
IMO B
