J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 9: EXERCISE

The speed of a boat in still water is $8 \mathrm{km}/\mathrm{h}$. It can go $15 \mathrm{km}$ upstream and $22 \mathrm{km}$ downstream in $5$ hours. If the speed of the stream is $k \mathrm{km}/\mathrm{h}$, then find the value of $k$.

A passenger train takes $2$ hours less for a journey of $300 \mathrm{km}$, if its speed is increased by $5 \mathrm{km}/\mathrm{h}$ from its usual speed. If its usual speed is $k \mathrm{km}/\mathrm{h}$, then find the value of $k$.

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

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 $30$ minutes less for the journey. If the original speed of the train is $k \mathrm{km}/\mathrm{hr}$, then find the value of $k$.

A motorboat whose speed is $9 \mathrm{km}/\mathrm{h}$ in still water, goes $15 \mathrm{km}$ downstream and comes back in a total time of $3$ hours $45$ minutes. If the speed of the stream is $k \mathrm{km}/\mathrm{hr}$, then find the value of $k$.

A motorboat whose speed is $18 \mathrm{km}/\mathrm{h}$ in still water, takes $1$ hour more to go $24 \mathrm{km}$ upstream than to return to the same point. If the speed of the stream is $k \mathrm{km}/\mathrm{hr}$, then find the value of $k$.

The distance between Mumbai and Pune is $192 \mathrm{km}$. Travelling by Deccan Queen, it takes $48$ minutes less than another train.If the speeds of the two trains differ by $20 \mathrm{km}/\mathrm{hr}$. And if the speed of the Deccan Queen is $k \mathrm{km}/\mathrm{h}$, then find the value of $k$.

An aeroplane left $50$ 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 $250 \mathrm{km}/\mathrm{h}$ from its usual speed. If the original speed of aeroplane is $k \mathrm{km}/\mathrm{hr}$, then find the value of $k$.