M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 5: Exercise 4.5

A train travels at a certain average speed for a distance of $63 \mathrm{km}$ and then travels a distance of $72 \mathrm{km}$ at an average speed of $6 \mathrm{km}/\mathrm{h}$ more than its original speed. If it takes $3 \mathrm{hours}$ to complete the journey, what is the original speed?

A bus travels at a certain average speed for a distance of $75 \mathrm{km}$ and the travels a distance of $90 \mathrm{km}$ at an average speed of $10 \mathrm{km}/\mathrm{h}$ more than its original speed. If it takes $3 \mathrm{hours}$ to complete the journey, what is its original average speed?

A motorboat whose speed is $24 \mathrm{km}/\mathrm{h}$ in still water, takes $1 \mathrm{hour}$ more to go $32 \mathrm{km}$ upstream than to return downstream to the same spot. Find the speed of the stream.

Speed of a boat in still water is $15 \mathrm{km}/\mathrm{h}$. It goes $30 \mathrm{km}$ upstream and returns back at the same point in $4 \mathrm{hours} 30 \mathrm{minutes}$. Find the speed of the stream.

A motor boat whose speed in still water is $9 \mathrm{km}/\mathrm{h}$, goes $15 \mathrm{km}$ downstream and comes back to the same spot in a total time of $3 \mathrm{hours} 45 \mathrm{minutes}$. Find the speed of the stream.

The sum of the areas of two squares is $640 {\mathrm{m}}^2$. If the difference of their parameter is $64 \mathrm{m}$, find the sides of the squares.

The sum of the areas of two squares is $157 {\mathrm{m}}^2$. If the sum of their parameter is $68 \mathrm{m}$, find the sides of the squares.

Two water pipes together can fill a tank in $1\frac{7}{8} \mathrm{hours}$. The tap with larger diameter takes $2 \mathrm{hours}$ less than the tap with smaller diameter to fill the tank separately. Find the time in which each tap can fill the tank separately.