Saket Sharma Solutions for Exercise 1: Exercise 1

A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train?
(Assume that the trains run at uniform speeds)

Walking at $60\%$ of his usual speed, a man reaches his destination $1 \mathrm{hour} 40 \mathrm{minutes}$ late. His usual time (in $\mathrm{hours}$) to reach the destination is:

A man starts from his house travelling at $30 \mathrm{km}/\mathrm{h}$, he reaches his office late by $10 \mathrm{minutes}$, and travelling at $24 \mathrm{km}/\mathrm{h}$, he reaches his office late by $18 \mathrm{minutes}$. The distance (in $\mathrm{km}$) from his house to his office is:

In a flight of $2400 km$, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $400 km/hr$ And the time of flight increased by $1$ Hours. The duration of the flight is:

Two vehicles $A$ and $B$ travel with uniform speed $30 km$ per hour and $60 km$ per hour respectively in the same direction. They start at the same time and from the same place for a distance of $120 km$. The faster vehicle $B$ reaches the destination and travels back with the same speed. Assume that the loss of time to change the direction is negligible. If the distance travelled by the slower vehicle $A$ before the two vehicles cross each other, then is

A car covers a certain distance in $8 \mathrm{h}$. If the speed is increased by $4 \mathrm{km}/\mathrm{h}$. The distance could be covered in $7\frac{1}{2} \mathrm{h}$. The distance is:

A circular field has a circumference of $360 km$. Three cyclists start together and can cycle $48, 60$ and $72 km$ a day, round the field. After how many days will they meet again?

Ravi travels 300 km partly by train and partly by car. He takes 4 hours to reach, if he travels 60 km by train and rest by car. He will take 10 minutes more if he were to travel 100 km by train and rest by car. The sped of the train and car is :