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A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?
- a)30 m
- b)16 m
- c)48 m
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B...
tunnel pq=16m,
a(s)= speed of rabbit a , similarly b(s) for rabbit b;
t(s)= speed of train.
now a and b are sitting at 12m and 8m away from the enterance from which train is coming, they will move to opposite ends.a towards p and b towards q and are caught by train at those ends. so we can say
when train moves x distance, a will move 12m and when train move x+16, b will move 8m.
now a(s)/t(s)-b(s)/t(s)=1/8
or time is same , use distance only in the speed formula
12/x-8/x+6=1/8; put the value of x from the options or make quadratic equation.
x=48 m
Most Upvoted Answer
A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B...
Given:
Length of tunnel PQ = 16m
Distance of Rabbit A from P = 12m
Distance of Rabbit B from P = 8m
Difference between the ratios of the speed of Rabbit A to that of train and the ratio of the speed of Rabbit B to that of train is 1/8
To Find:
Distance x from point P where the train is when both the rabbits get caught at the ends of the tunnel.
Solution:
Let the speed of the train be Vt m/s, the speed of Rabbit A be Va m/s, and the speed of Rabbit B be Vb m/s.
When Rabbit A starts running towards P, the relative speed of A with respect to the train is Va - Vt
When Rabbit B starts running towards Q, the relative speed of B with respect to the train is Vb + Vt
Let the time taken by both rabbits to reach the end of the tunnel be t seconds.
Distance covered by Rabbit A in t seconds = 12 + Va * t
Distance covered by Rabbit B in t seconds = 8 + Vb * t
Distance covered by the train in t seconds = x
As both rabbits get caught at the ends of the tunnel,
12 + Va * t + 16 = 8 + Vb * t
=> Va * t - Vb * t = -4
Given, (Va/Vt) - (Vb/Vt) = 1/8
=> Va - Vb = Vt/8
Solving the above two equations, we get
Va = (Vt/16) + 1/2
Vb = (Vt/16) - 1/2
Now, substituting the values of Va and Vb in the equation Va * t - Vb * t = -4, we get
t = 8/Vt
Substituting the value of t in the distance equation for the train, we get
x = Vt * t = Vt * 8/Vt = 8
Therefore, the distance x from point P where the train is when both the rabbits get caught at the ends of the tunnel is 8m.
Hence, the correct option is (c) 48m.
Length of tunnel PQ = 16m
Distance of Rabbit A from P = 12m
Distance of Rabbit B from P = 8m
Difference between the ratios of the speed of Rabbit A to that of train and the ratio of the speed of Rabbit B to that of train is 1/8
To Find:
Distance x from point P where the train is when both the rabbits get caught at the ends of the tunnel.
Solution:
Let the speed of the train be Vt m/s, the speed of Rabbit A be Va m/s, and the speed of Rabbit B be Vb m/s.
When Rabbit A starts running towards P, the relative speed of A with respect to the train is Va - Vt
When Rabbit B starts running towards Q, the relative speed of B with respect to the train is Vb + Vt
Let the time taken by both rabbits to reach the end of the tunnel be t seconds.
Distance covered by Rabbit A in t seconds = 12 + Va * t
Distance covered by Rabbit B in t seconds = 8 + Vb * t
Distance covered by the train in t seconds = x
As both rabbits get caught at the ends of the tunnel,
12 + Va * t + 16 = 8 + Vb * t
=> Va * t - Vb * t = -4
Given, (Va/Vt) - (Vb/Vt) = 1/8
=> Va - Vb = Vt/8
Solving the above two equations, we get
Va = (Vt/16) + 1/2
Vb = (Vt/16) - 1/2
Now, substituting the values of Va and Vb in the equation Va * t - Vb * t = -4, we get
t = 8/Vt
Substituting the value of t in the distance equation for the train, we get
x = Vt * t = Vt * 8/Vt = 8
Therefore, the distance x from point P where the train is when both the rabbits get caught at the ends of the tunnel is 8m.
Hence, the correct option is (c) 48m.
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A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer?.
A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are standing at points which are 12 m and 8 m inside the tunnel with respect to the entrance P. When the train is x m away from P, A starts running towards P and B towards Q. Difference between the ratios of the speed of A to that of the train and the ratio of the speed of B to that of train is 1/8. How much can the distance x be, if both of them get caught at the ends of the tunnel?a)30 mb)16 mc)48 md)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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