The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 315 and for a journey of 15 km, the charge paid is ₹ 465. What are the fixed charges and the charge per kilometer ? How much does a person have to pay for travelling a distance of 32 km ?

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Geeta paid ₹ 27 for a book kept for seven days, while Mohit paid ₹ 21 for the book he kept for five days. Find the fixed charges and the charge for each extra day.

The area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?