# Research Methodology

1. The monthly income of two persons are in the ratio 4:5 and their monthly expenditures are in the ratio 7:9. If each saves Rs. 50 per month, find their monthly incomes.

2. A tour operator charges Rs. 136 per passenger for 100 passengers with a discount of rs. 4 for each 10 passengers in excess of 100. Determine the number of passengers that will maximize the amount of money the tour operator services.

3. A firm has current sales of Rs. 50000 e0.02t per month. The firm wants to embark upon a certain advertising campaign that will increase the sales by 2% every month over the 12 months period of campaign. Find total increase of sales as a result of the campaign.

4. There are two branches of an establishment employing 200 and 160 persons respectively. If the AMs of the monthly salaries paid by the two branches are Rs. 550 and Rs. 450 respectively, find AM of the salaries of the employees of the establishment as a whole.

5. Calculate the median for the following frequency distribution

 Marks 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 No of students 7 15 24 31 42 30 26 15 10

6. For the cost function y = 500x – 40x² + 3x³ for x units, find the average cost, marginal cost and marginal average cost.

7. A man borrows Rs. 1500 and agrees to repay the debt in 5 equal installments with 6% interest, compounded annually. If the first payment is to be made at the end of the first year, how much should each payment be?

8. A manufacturer can sell x items per month at a price of P = 300 – 2x rupees. Producing x items cost the manufacturer y rupees where y = 2x + 1000. How much production will yield maximum profit.