Represent the following situations mathematically: A toys industry produces a certain number of toys in a day. The cost of production of each toy (in rupese) 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.

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 ? 90, find the number of articles produced and the cost of each article.

A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?

Represent the following situations mathematically: 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.

Solve the problems, 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.

Following is the distribution of the number of out-door patients registered in a certain hospital in 100 days : Find the arithmetic mean and standard deviation.

A fruit vendor buys some oranges at the rate of Rs 5 per orange. He also buys an equal number of bananans at the rate of Rs 2 per banana. He makes a 20% profit on orange and a 15% profit on bananas. At the end of the day, all the fruit is sold out. His total profit is Rs 390. Find the number of oranges purchased.

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on secnd machine. Each unit of product A is sold at Rs 7 profit and that of B at a profit of Rs 4. Find the production level per day for maximum profit graphically.