Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
How can Arya divide his sandwiches so that each person has an equal share?

Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich. What part of a sandwich will each boy receive?

A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each on the three machines are given in the following table: SHe makes a profit of Rs 600 and Rs 400 on items M and N respectively. How many of each item should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum Profit?

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (4, 3).

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (3, 4).

A manufacturer considers that men and women are equally efficient and so he pays them at the same rate. He has 30 and 27 units of workers ( male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital are required to produce one unit of B. If A and B are priced at Rs 100 and Rs 120 per unit respectively, how should he use his resources to maximise the total revenue? From the above as as LPP and solve graphically. Do you agree with this view of the manufacturer that men and women are equally efficient and so should be paid at the same rate?

A manufacturing company makes two types of television sets, one is black and white and the other is colcoured. The company has resources to make atmost 300 sets a week. It takes Rs.1800 to make a black and white set and Rs.2700 to make a colured set. The company can spend not more thatn Rs.648000 a week to make television sets. if it makes a profit of Rs.510 per black and white set and Rs.675 per coloured set. how many sets of each type should be produced so that the company has maximum profit?