Jaidev takes 2 ̶ 1/5 minutes to walk across the school ground. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the start- ing point?

A factor manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to maufacture a package of screw s A, while it take 6 minutes on automatic and 3 minutes on the hand operated machines to maufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs. 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screw he manufactures, how many packages of each type should the factory owner produced day in order to maximise his profit? Determine the maximum profit.

A body slides down from rest along a smooth inclined plane making an angle of 45^(@) with the horizontal and takes time 'Y' to slide down the whole length of the plane. If the plane surface is rough the same body takes n.t time to slide down same length of the plane where n is a number greater than one. What is the value of coefficient of friction between the body and rough plane surface?

In a first-order reaction, it takes the reactant 40.5 minutes to be 25% decomposed. Find the rate constant of the reaction.

Salma takes 15 minutes from her house to reach her school on a bicycle. If the bicycle has a speed 2m//s, calculate the distance between her house and the school.

Two vessels of different materials are identical in size and wall thickness. They are filled with equal quantities of ice at 0°C. The ratio of their thermal conductivities is 5 : 2. If it takes 10 minutess for the ice to melt in the first vessel, then find what time the ice in the vessel takes to melt.

A factory makes tennis rackets and cricket bats . A tennis racket takes 1.5 h of machine time and 3 h of craftman's time in its making while a cricket bat takes 3 h of machine time and 1 h of craftman' time . In a day , the factory has the availability of not more than 42 h of machine time and 24 h of craftman's time (a) What number of rackets and bats must be made, if the factory is to work at full capacity? (b) If the profits on rackets and on bats is Rs 20 and Rs 10 respectively , find the maximum profit of the factory when it works at full capacity .

Priya travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Formulate the following problems as a pair of equations, and hence find their solutions : Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.