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11 Jul 2019, 07:44
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
67% (03:06) correct
33%
(03:22)
wrong
based on 183
sessions
History
Date
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It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
A. 2 : 3
B. 3 : 2
C. 3 : 4
D. 4 : 3
E. 3 : 9
A. 2 : 3
B. 3 : 2
C. 3 : 4
D. 4 : 3
E. 3 : 9
11 Jul 2019, 11:32
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Speed of train=T
Speed of car= C
(120/T)+(480/C)= 8......(1)
Also, 80/T-80/C=1/3 or (480/T)-(480/C)=2......(2)
Add (1) and (2)
600/T=10
T=60
C=80
T/C=3/4
Speed of car= C
(120/T)+(480/C)= 8......(1)
Also, 80/T-80/C=1/3 or (480/T)-(480/C)=2......(2)
Add (1) and (2)
600/T=10
T=60
C=80
T/C=3/4
dharam44
General Discussion
11 Aug 2020, 13:05
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dharam44
Solution
- • Let us assume that the speed of the train is \(s_t\) km per hour and
- o The speed of the car is \(s_c\) km per hour.
Scenario 1
- • \( \frac{120}{s_t} + \frac{480}{s_c} = 8\)
• \(⟹ \frac{1}{s_t} + \frac{4}{s_c} = \frac{8}{120}…………Eq.(i)\)
Scenario 2
- • \( \frac{200}{s_t} + \frac{400}{s_c} = 8 +\frac{1}{3}\)
• \(⟹ \frac{1}{s_t} + \frac{2}{s_c} = \frac{25}{600}…………Eq.(ii)\)
• Now, subtracting Eq.(ii) from Eq.(i), we get,
- o \( \frac{2}{s_c} =\frac{8}{120} - \frac{25}{600}\)
\(⟹ \frac{2}{s_c} =\frac{15}{600}\)
\(⟹ s_c = 80\)
• Substituting the value of \(s_c\) in Eq.(i), we get,
- o \( \frac{1}{s_t} + \frac{4}{80} = \frac{8}{120} ⟹ s_t = 60\)
• Therefore, \(\frac{s_t}{s_c} = \frac{60}{80} = \frac{3}{4}\)
Thus, the correct answer is Option C.
