R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 8: EXERCISE 4.8

A fast train takes one hour less than a slow train for a journey of $200 \mathrm{km}$. If the speed of the slow train is $10 \mathrm{km}/\mathrm{hr}$ is less than that of the fast train, find the speed of the two trains.

A train covers a distance of $90 \mathrm{km}$ at a uniform speed. Had the speed been $15 \mathrm{km}/\mathrm{hour}$more, it would have taken $30 \mathrm{minutes}$ less for a journey. Find the original speed of the train.

A train travels $360 \mathrm{km}$ at a uniform speed. If the speed had been $5 \mathrm{km}/\mathrm{hr}$ more, it would have taken $1 \mathrm{hour}$less for the same journey. Find the speed of the train.

An express train takes$1 \mathrm{hour}$ less than a passenger train to travel $132 \mathrm{km}$ between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $11 \mathrm{km}/\mathrm{hr}$ more than that of the passenger train, find the average speed of two trains.

An aeroplane left $50 \mathrm{minutes}$ later than its scheduled time, and in order to reach the destination, $1250 \mathrm{km}$ away, in time, it had to increase its speed by $250 \mathrm{km}/\mathrm{hr}$ from its usual speed. Find its usual speed.

While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by $30$ minutes to reach the destination, $1500 \mathrm{km}$ away in time, the pilot increased the speed by $100 \mathrm{km}/\mathrm{hr}$. Find the original speed/hour of the plane.

A motor boat whose speed in still water is $18 \mathrm{km}/\mathrm{hr}$ takes $1$ hour more to go $24 \mathrm{km}$ upstream than to return downstream to the same spot. Find the speed of the stream.

A car moves a distance of$2592 \mathrm{km}$ with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in $\mathrm{km}/\mathrm{hour}$. Find the time taken to cover the distance.