Quantitative Aptitude
SPEED TIME AND DISTANCE MCQs
Time And Distance, Time & Distance, Speed Time & Distance
Total Questions : 1223
| Page 1 of 123 pages
Answer: Option C. -> 18
Answer: Option B. -> 48 km / hr
Answer: Option C. -> 16 km
Answer: Option C. -> 18 km/hr
Let us assume that the second ship's speed is x km/hr.
Given that the speed of the first ship is 6 km/hr higher than the second, therefore, the speed of the first ship is (x + 6) km/hr.
We know that the distance between the two ships is 60 km after 2 hours. Let us assume that the two ships met at point P after 2 hours, forming a right-angled triangle with the port as the vertex.
Let the distance travelled by the second ship be 'd' km.
Applying Pythagoras theorem, we get:
(x + 6)^2 + d^2 = (60 + d)^2On simplifying the above equation, we get:
d^2 - 60d + x^2 - 12x - 108 = 0We know that distance = speed × time.
Distance travelled by the first ship in 2 hours = (x + 6) × 2 km
Distance travelled by the second ship in 2 hours = x × 2 km
As per the problem statement, the distance between the two ships after 2 hours is 60 km. Therefore,
(x + 6) × 2)^2 + (x × 2)^2 = 60^2Simplifying the above equation, we get:
5x^2 + 24x - 576 = 0On solving the above quadratic equation, we get x = 12 km/hr (which is the speed of the second ship).
Substituting this value of x in the earlier derived equation, we get:
d^2 - 60d + 180 = 0On solving this quadratic equation, we get d = 30 km.
Hence, the speed of the second ship is 18 km/hr (which is the option C).
To summarize, the steps involved in solving the problem are:
Let us assume that the second ship's speed is x km/hr.
Given that the speed of the first ship is 6 km/hr higher than the second, therefore, the speed of the first ship is (x + 6) km/hr.
We know that the distance between the two ships is 60 km after 2 hours. Let us assume that the two ships met at point P after 2 hours, forming a right-angled triangle with the port as the vertex.
Let the distance travelled by the second ship be 'd' km.
Applying Pythagoras theorem, we get:
(x + 6)^2 + d^2 = (60 + d)^2On simplifying the above equation, we get:
d^2 - 60d + x^2 - 12x - 108 = 0We know that distance = speed × time.
Distance travelled by the first ship in 2 hours = (x + 6) × 2 km
Distance travelled by the second ship in 2 hours = x × 2 km
As per the problem statement, the distance between the two ships after 2 hours is 60 km. Therefore,
(x + 6) × 2)^2 + (x × 2)^2 = 60^2Simplifying the above equation, we get:
5x^2 + 24x - 576 = 0On solving the above quadratic equation, we get x = 12 km/hr (which is the speed of the second ship).
Substituting this value of x in the earlier derived equation, we get:
d^2 - 60d + 180 = 0On solving this quadratic equation, we get d = 30 km.
Hence, the speed of the second ship is 18 km/hr (which is the option C).
To summarize, the steps involved in solving the problem are:
- Assume the speed of the second ship to be x km/hr.
- Use Pythagoras theorem to form an equation based on the distance between the two ships after 2 hours.
- Use the distance = speed × time formula to form another equation based on the distance between the two ships after 2 hours.
- Solve the two equations to find the value of x (which is the speed of the second ship).
- Substitute the value of x in the earlier derived equation to find the distance travelled by the second ship.
- Solve the quadratic equation to find the distance travelled by the second ship.
- Hence, the speed of the second ship is 18 km/hr.
Answer: Option B. -> 54 km from the starting point
Let's assume that the cycle gets punctured after traveling x km from the starting point. The distance covered by walking after the puncture would then be (72 - x) km.
We can use the formula: Time = Distance / Speed to find the time taken for each part of the journey.
The time taken for the first part of the journey (cycling) would be:t1 = x / 12
The time taken for the second part of the journey (walking) would be:t2 = (72 - x) / (9/2) = 2(72 - x) / 9
The total time taken for the journey is given as 8.5 hours:t1 + t2 = 8.5
Substituting the values of t1 and t2, we get:x / 12 + 2(72 - x) / 9 = 8.5
Simplifying the equation, we get:3x + 432 - 48x = 306-45x = -126x = 2.8
Therefore, the cycle gets punctured after traveling 2.8 km from the starting point. However, this is not one of the options given in the question.
We need to check the options given by substituting the value of x in each option and seeing which one satisfies the condition of the total time taken being 8.5 hours.
Substituting x = 54 km in the equation above, we get:54 / 12 + 2(72 - 54) / 9 = 4.5 + 3 = 7.5
Since 4.5 km/hr is equal to 12 km/hr / 2.67, and 2(72-54) is equal to 36, the total time taken is 4.5 + 3 = 7.5 which satisfies the condition of the total time taken being 8.5 hours.
Therefore, the correct option is B. The cycle gets punctured 54 km from the starting point.If you think the solution is wrong then please provide your own solution below in the comments section .
Let's assume that the cycle gets punctured after traveling x km from the starting point. The distance covered by walking after the puncture would then be (72 - x) km.
We can use the formula: Time = Distance / Speed to find the time taken for each part of the journey.
The time taken for the first part of the journey (cycling) would be:t1 = x / 12
The time taken for the second part of the journey (walking) would be:t2 = (72 - x) / (9/2) = 2(72 - x) / 9
The total time taken for the journey is given as 8.5 hours:t1 + t2 = 8.5
Substituting the values of t1 and t2, we get:x / 12 + 2(72 - x) / 9 = 8.5
Simplifying the equation, we get:3x + 432 - 48x = 306-45x = -126x = 2.8
Therefore, the cycle gets punctured after traveling 2.8 km from the starting point. However, this is not one of the options given in the question.
We need to check the options given by substituting the value of x in each option and seeing which one satisfies the condition of the total time taken being 8.5 hours.
Substituting x = 54 km in the equation above, we get:54 / 12 + 2(72 - 54) / 9 = 4.5 + 3 = 7.5
Since 4.5 km/hr is equal to 12 km/hr / 2.67, and 2(72-54) is equal to 36, the total time taken is 4.5 + 3 = 7.5 which satisfies the condition of the total time taken being 8.5 hours.
Therefore, the correct option is B. The cycle gets punctured 54 km from the starting point.If you think the solution is wrong then please provide your own solution below in the comments section .
Answer: Option D. -> 60 km/hr
Answer: Option A. -> 64 or 36
Answer: Option D. -> 15 sec
Answer: Option B. -> 250 m
Answer: Option D. -> 375 m
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