A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90. find the number of articles produced and the cost of each article.

(A)John and Jivanti together have 45 marbles, Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. (2) A cottage industry produces a cartain number of toys in a day. The cost of production of each toy (in rupee) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs.750. We would like to find out the number of toys produced on that day.

Manufacturer can sell x items at a price of rupees (5-(x)/(100)) each. The cost price of x items is Rs. ((x)/(5)+500) . Find the number of items he should sell to earn maximum prodit.

On the occasion of New year's day a sweet stall prepared sweet packets. Number of sweet packets and cost of each packet are given as follows. Find the mean, median and mode of the data.

A small firm manufacturers Golden chains and rings. The total number of chains and rings that it can manufacture in a day is at the most 24. The ring takes 30 minutes. The maximum time available per day is 16 hours. If the profit on the ring be Rs. 300 and one chain be Rs. 190. How many of rings and chains be produced to maximize the profit ?

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

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

A manufacturer produces nuts and bolts. It takes 1 hour of worl in machine A and 3 hours on machine B to produce a package of nuts. It take 3 hours on machien A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise bis profit, if he operates his machines for at the most 12 hours a day?

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day ?

Represent the folloowing situations in the form of quadratic equations : (1) The length of the hypotenus of an isosceles right angled triangle is 10 cm. We need to find the length of each of two equal sides. (2)The sum of squares of two consecutive odd positive integers in 970. We need to find those integers. (3) While selling an article for Rs. 96, the profit in percentage is equal to its cost price in rupees. We need to find the cost price of the article. (4) When there is a decreases of 10 km/h in the usual speed of a train, it takes 4(1)/(2) hours more to cover 900km. We need to find the usual speed of the train. (5) The sum of squares of two parts of 31 is 481. We need to find those two parts.

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs. 5 and that from a shade is Rs. 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit ?