Question : In a 5 km race, S gave a 500 m head start to T. If they finished the race at the same time and the speed of T is 13.5 km/hr, the speed of S is:
Option 1: 15 km/hr
Option 2: 20 km/hr
Option 3: 17.5 km/hr
Option 4: 16.5 km/hr
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Correct Answer: 15 km/hr
Solution : Let the speed of S as \(v\) km/hr. Given that S gave a 500 m (or 0.5 km) head start to T, S has to run 5 km while T runs 4.5 km. Since they finish the race at the same time, their times are equal. $⇒\frac{\text{Distance of S}}{\text{Speed of S}} = \frac{\text{Distance of T}}{\text{Speed of T}}$ Substituting the given values into the equation, $⇒\frac{5}{v} = \frac{4.5}{13.5}$ $⇒v = \frac{5 \times 13.5}{4.5} = 15 $ Hence, the correct answer is 15 km/hr.
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Question : Zeenat and Nasreen participate in a circular race of 1.2 km. They start the race at a speed of 18 km/hr and 27 km/hr respectively, from the same point at the same time. After how much time (in minutes) will they meet at the starting point for the first time, if they are running in the same direction?
Option 1: 9
Option 2: 7
Option 3: 10
Option 4: 8
Question : One-third part of a certain journey is covered at the speed of 10 km/hr, one-fourth part at the speed of 15 km/hr, and the rest part at the speed of 20 km/hr. What will be the average speed (in km/hr) for the whole journey?
Option 1: $15$
Option 2: $\frac{200}{17}$
Option 3: $\frac{240}{17}$
Option 4: $\frac{280}{17}$
Question : A boat can move upstream at 25 km/hr and downstream at 35 km/hr. What is the speed of the current?
Option 1: 10 km/hr
Option 2: 15 km/hr
Option 3: 5 km/hr
Option 4: 22.5 km/hr
Question : A ship goes at 18 km/hr downstream and at 16 km/hr upstream. What will be the speed of the ship in still water?
Option 1: 14 km/hr
Option 2: 17 km/hr
Option 3: 16 km/hr
Option 4: 15 km/hr
Question : A boy covers a certain distance between his house and school on a cycle. Riding at an average speed of 15 km/hr, he is late by 10 min. However, with an average speed of 20 km/hr, he reaches the school 5 min earlier. Find the distance between his house and school.
Option 1: 25 km
Option 2: 20 km
Option 3: 15 km
Option 4: 30 km
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