B Nirmala Shastry Solutions for Exercise 2: EXERCISE 5B

A fractions' value of $\frac{4}{5}$.When its numerator is increased by $9$, the new fraction equals the reciprocal of the value of the original fraction. Find the original fraction.

A boat takes $6$ hours to travel $36 km$ upstream and it takes $3$ hours to travel $30 km$ downstream. Find the speed of the boat in still water and the speed of the stream.

A plane can fly $1120 km$ in $1$ hour $20$ minutes with the wind. Flying against the same wind, the plane travels the same distance in $1$ hour $24$ minutes. Find the speed of the plane and the speed of the wind.

If Laisha walks for $1$ hour and cycles for $2$ hours she can travel $33 km$. But if she walks for $2$ hours and cycles for $1$ hour she can cover $24 km$. What are her walking and cycling speeds?

An aeroplane takes $3$ hours to fly $1200 km$ against the wind. The return trip takes $2$ hours. Find the speed of the plane in still air and the wind speed.

A train covers a certain distance at a uniform speed. If the train had been $20 km/h$ faster, it would had taken $4$ hours less than the scheduled time. If the train were slower by $10 km/h$, it would had taken $4$ hours more than the scheduled time. Find the distance covered.

Maheep travels $600 km$ partly by train and partly by car. He takes $8$ hours to cover the whole distance if he travels $120 km$ by train and rest by car. But he takes $20$ minutes longer if he travels $200 km$ by train and the rest by car. Find the speed of train and car.

Two towns $A$ and $B$ are $120 km$ apart on the highway. One car starts from $A$ and the other from $B$ at the same time at different speeds. If the car travels in the same direction, the car meets in $4$ hours. But when they travel towards each other, they meet in $1$ hour. Find their speeds.