The parking charges of a car in Hyderabad Railway station for first two hours is 50 and 10 for each subsequent hour. Write down an equation and draw the graph. Find the following charges from the graph
(i) For three hours (ii) For six hours
(iii) How many hours did Rekha park her car if she paid 80 as parking charges?

A lending library has fixed charge for the first three days and an additional charges for each day thereafter. John paid 27 for a book kept for seven days. If the fixed charges be x and subsequent per day charges be y, then write the linear equation representing the above information and draw the graph of the same. From the graph, find fixed charges for the first three if additional charges for each day thereafter is 4. Find additional charges for each day thereafter if the fixed charges for the first three days of 7.

An auto charges 15 for first kilometer and 8 each for each subsequent kilometer. For a distance of ‘x’ km. an amount of ‘y’ is paid. Write the linear equation representing this information and draw the graph. With the help of graph find the distance travelled if the fare paid is 55? How much would have to be paid for 7 kilometers?

(Manufacturing problem) 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 atleast 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N 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 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 ?

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?