A man requires 9 days less than his son to complete a job. Together, they can finish the job in 20 days. How many days would each require to finish the job alone?

Riyas calculates the total length of uniform cloth required for the students of his class. Boys require 1.25 metres each and girls require 1.75 metres each. There are 20 boys and 23 girls in the class. Then how many metres of cloth are required in all?

A factory manufactures two types of screws, A and B . Each type of screw requires the two machines, an automatic and a hand operated.It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screw A at a profit of Rs 7 and screws B at a profit of Rs 10 . Assuming that he can sell all the screws he manufactures, how many packages of eách type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

A firm manufactures two types of products A and B and sells them at a profit of Rs. 5 per unit of type A and Rs. 3 per unit of type B . Each product is processed on two machines M_1 and M_2 . One unit of type A requires one minute of processing time, on, M_1 and two minutes of processing time on M_2 whereas one unit of type B requires one minute of processing time on M_1 and one minute of M_2 . Machines M_1 and M_2 are respectively available for at most 5 hours and 6 hours a day. Find how many, units of each type of product should the firm produce a day, in order, to maximise the profit. Solve thè problem graphically.

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day 4 more workers dropped out on thrid day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed

150 workers were engaged to finish a job in a certain number of days. 4 , workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

(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 where as 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 item should she produce so as to maximise her profit assuming that she can swll all the items that she produced ? What will be the maximum profit ?

A manufacturur 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 per package on bolts.How many package of each should be produced each day so as to maximise the profit,if he operates his machine for at the most 12 hours a days? By suitable defining the variables write the objective function of the problem.

A manufacturur 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 per package on bolts.How many package of each should be produced each day so as to maximise the profit,if he operates his machine for at the most 12 hours a days? Solve the LPP graphically and find the number of packages of nuts and bolts to be manufactured.

John and Ramesh took up a job on contract. John worked 7 days and Ramesh 6 days. They got 6500 rupees as wages which they divided in the ratio of the number of days each worked. How much did each get?

A man ate 100 grapes in 5 days. Each day he ate 5 more than what he ate the previous day. Can you find the number of grapes he ate eạch day?