The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.

Two factories decided to award their employees for three values of (a) adaptable to new techniques (b) careful and alert in difficult situations keeping calm in tense situations. At the rate of Rs, x, Rs, y, and Rs z per person respectivley. The first factory decided to honour respectively 2,4, and 3 employees with a total prize money of Rs. 29000. the second factory decided to honour respectively 5,2 and 3 employees with the prize money of Rs 30500. If the three prizes per person together cost Rs 9500, then solve these equations using matrices.

Two factories decided to award their employees for three values of (a) adaptable to new techniques (b) careful and alert in difficult situations keeping calm in tense situations. At the rate of Rs, x, Rs, y, and Rs z per person respectivley. The first factory decided to honour respectively 2,4, and 3 employees with a total prize money of Rs. 29000. the second factory decided to honour respectively 5,2 and 3 employees with the prize money of Rs 30500. If the three prizes per person together cost Rs 9500, then which values are reflected in the question?

Deveshi has a total of Rs 590 as currency notes in the denominations of Rs 50, Rs 20 and Rs 10. The ratio of the number of Rs 50 notes and Rs 20 notes is 3:5. If she has a total of 25 notes, how many notes of each denomination she has?

A merchant planes to sell two types of personal computers -a desktop model and a portain model that will cost Rs. 2500 and Rs. 40000 respectively. He estimates that the total montain demand of computers will not exceed 250 units. Determine the number of units of easy type of computers which the merchant should stock to get maximum profit it he does want to invest more than Rs. 70 lakhs and if his profit on the desktop model is Rs. 4500 on portable model is Rs. 5000. Make an L.P.P and solve it graphically.

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

In a hockey match two teams A and B scored same number of goals upto the end of the games so as to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

A finance company has offices located in every division, every district and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superintendent, two clerks, one typist and one peon. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendent Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix notation find The total number of posts of each kind in all the offices taken together,

In each of the following problems, clearly state what the relevant and irrelevant factors are while going through Steps 1, 2 and 3 given in this chapter :- Suppose a company needs a computer for some period of time. The company can either hire a computer for Rs 2,000 per month or buy one for Rs 25,000. If the company has to use the computer for a long period, the company will pay such a high rent, that buying a computer will be cheaper. On the other hand, if the company has to use the computer for say, just one month, then hiring a computer will be cheaper. Find the number of months beyond which it will be cheaper to buy a computer.