A trust fund has Rs. 30,000 that must be invested in two different types of bonds . The first bond pays `5%` interest per year ,and the second bond pays `7%` interest per year .Using matrix multiplication , determine how to divide Rs. 30,000 among the two types of bonds . If the trust fund must obtain an annual total interest of : (a) Rs 1800 (b) Rs. 2000

A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests for an AP. If so , find the interest at the end of 30 years making use of this fact.

In which of the following situations, does the list of numbers involved make an arithmetic progression , and why ? The amount of money in the account every year, when Rs 10,000 is deposited at compound interest at 8% per annum.

A manufacturer produces two models of bikes model X and model Y. Model X takes a 6 man hours to make per unit, while Model Y takes 10 man-hours per unit. There is a total of 450 man-hour available per week. Handling and Marketing costs are Rs. 2000 and Rs. 1000 per unit for Models X and Y respectively. The total funds available for these purposes are Rs. 80,000 per week. Profits per unit for Models X and Y are Rs. 1000 and Rs. 500, respectively. How many bikes of each model should the manufacturer produce, so as to yield a maximum profit ? Find the maximum profit.

A manufacturer makes two type of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below : Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs. 7.50 and that on each toy of type B is Rs. 5, whow that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.