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20 Apr 2020, 06:43
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (02:59) correct
65%
(03:11)
wrong
based on 86
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Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?
A. 20 kmph
B. 40 kmph
C. 50 kmph
D. 60 kmph
E. 80 kmph
Are You Up For the Challenge: 700 Level Questions
A. 20 kmph
B. 40 kmph
C. 50 kmph
D. 60 kmph
E. 80 kmph
Are You Up For the Challenge: 700 Level Questions
20 Apr 2020, 07:42
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Let say Speed of Car1 = X km/Hr
Let say Speed of Car2 = Y km/Hr
Let say speed of car3 = Z km/Hr
Let say distance between AB = D km/Hr
Time taken by Car 1 = D/X
Time taken by Car 2 = D/Y
Time taken by Car 3 = D/Z
D/Z - D/Y = D/Y - D/X
=> 2/Y = 1/X + 1/Z ------------ (1)
Time taken by car 2 for 240 km = 240/Y
Time taken by Car 1 for 240 km = 240/X
240/X = 240/Y + 1
=> 1/X - 1/240= 1/Y ------------ (2)
Putting 1/Y in eq 1
2/X - 1/120 = 1/X + 1/Z
=> 1/X = 1/Z + 1/120 ------------ (3)
When 1st & Third car meet
Distance traveled by third car = 240 + 80 = 320 km
Distance traveled by First Car = 240 - 80 = 160 km
Time taken by both car is equal
320/Z = 160/X
=> Z = 2X
putting in eq 3
=> 1/X = 1/2X + 1/120
multiplying by 120X
=> 120 = 60 + X
=> X = 60
Z = 2X = 120
Z - X = 120 - 60 = 60 km/Hr
correct answer D
Let say Speed of Car2 = Y km/Hr
Let say speed of car3 = Z km/Hr
Let say distance between AB = D km/Hr
Time taken by Car 1 = D/X
Time taken by Car 2 = D/Y
Time taken by Car 3 = D/Z
D/Z - D/Y = D/Y - D/X
=> 2/Y = 1/X + 1/Z ------------ (1)
Time taken by car 2 for 240 km = 240/Y
Time taken by Car 1 for 240 km = 240/X
240/X = 240/Y + 1
=> 1/X - 1/240= 1/Y ------------ (2)
Putting 1/Y in eq 1
2/X - 1/120 = 1/X + 1/Z
=> 1/X = 1/Z + 1/120 ------------ (3)
When 1st & Third car meet
Distance traveled by third car = 240 + 80 = 320 km
Distance traveled by First Car = 240 - 80 = 160 km
Time taken by both car is equal
320/Z = 160/X
=> Z = 2X
putting in eq 3
=> 1/X = 1/2X + 1/120
multiplying by 120X
=> 120 = 60 + X
=> X = 60
Z = 2X = 120
Z - X = 120 - 60 = 60 km/Hr
correct answer D
