Today, we are focussing on Time-Speed-Distance problems. Here are five different kinds:
Question 1
A carriage in a fog passed a man walking at 3 kmph in the same direction. He could see the carriage for four minutes and it was visible to him up to a distance of 100 metres. What was the speed of the carriage?
(A) 5.2 kmph
(B) 4.5 kmph
(C) 4 kmph
(D) None of these
Question 2
A person drives to work at an average speed of 48 kmph. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?
(A) 30 km
(B) 40 km
(C) 45 km
(D) 48 km
Question 3
A train completes a journey with a few stoppages in between at an average speed of 40 kmph. If it had not stopped anywhere, it would have completed the journey at an average speed of 60 kmph. On an average, how many minutes per hour does the train stop for during the journey?
(A) 20 minutes
(B) 18 minutes
(C) 15 minutes
(D) 10 minutes
Question 4
A student reaches his classroom from his hostel three minutes late by walking at a speed of 5 kmph, but 7 minutes early by walking at 6 kmph. What is the distance of the class from the hostel?
(A) 4 km
(B) 5 km
(C) 6 km
(D) 7 km
Question 5
Aryan starts running at a speed of 40 metres per minute. Rahul follows him from the same starting point five minutes later. Rahul runs at 50 metres/min. Rahul’s dog also starts with Rahul and runs at 60 metres/min. The dog reaches Aryan and then comes back to Rahul, and he continues to run between Aryan and Rahul till Rahul reaches Aryan. What is the total distance covered by the dog until Rahul reaches Aryan?
(A) 600 metres
(B) 800 metres
(C) 1000 metres
(D) 1200 metres
N.B. Please note that the official timings for publication of these questions is 11 am daily.
SOLUTIONS TO DAILY CSAT MISSION # 78
1. (C) 2. (B) 3. (D) 4. (D) 5. (C)
Explanations
1. In option (A), P is with A and D in a team. This means R cant have either A or D or both in his team. So, this option is eliminated.
In option (B), P is in the same team as E. Since this cannot happen, this option is eliminated.
In option (C), everything is good.
In option (D), if P, Q and R form a team, there will be no captain in this team. So, this option is eliminated.
2. C and D cannot be in one team as they are both captains.
3. In option (A), P is in the same team as E. Since this cannot happen, this option is eliminated.
In option (B), R, E and S form a team. This means R does not have either A or D or both in his team. So, this option is eliminated.
In option (C), R, E and Q form a team. This means R does not have either A or D or both in his team. So, this option is eliminated.
In option (D), nothing is violated and all is well.
4. In option (D), P is ending up in the Royals team with A and E. Since P and E can’t be together, this division of people is not possible.
5. Let the vessel initially contain 4 litres of water and 7 litres of syrup (total: 11 litres).
Let ‘x’ litres of the mixture has been replaced with water. ‘x’ litres of the mixture will contain 4x/11 amount of water and 7x/11 amount of syrup.
Now, quantity of water in the new mixture = (4 – 4x/11 + x) litres.
And, quantity of syrup in the new mixture = (7 – 7x/11) litres.
Given, the quantities of water and syrup in the new mixture are equal (50% each). So (4 – 4x/11 + x) = (7 – 7x/11), which gives ‘x’ = 33/14.
Part of the mixture replaced = x/(Total volume of the mixture) = (33/14)/11 = 3/14.
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