Total expenditure (in Rs.) and its proportionate expenditures of two different months are given below:

Draw a component bar chart showing total expendicular and its proportionate expenditures.

Show that the height of a cylinder of given total surface area and open at the top has maximum volumes is equal to the radius of its base .

Puja, Uttam and Bireendra started a pertnership business with capital ₹ 5000, ₹ 7000 and ₹ 10000 respectively by this condition that (i) the monthly expenditure of managing the business is ₹125, (ii) Puja and uttam will gety ₹ 200 each per month for keeping the accounts upto date. If at the end of the year the total profit of the business be ₹ 6960, then find the share of profit of each of them.

A short bar magnet placed on a horizontal plane has its axis aligned along the magnetic north- south direction . Null points are found on the magnet . The earth's magnetic field at the place is 0.36G . What is the magnet at the total magnetic field on the normal bisector of the same distance as the null points (i.e., 14 cm) from the centre of the magnet (at null points , field due to a magnet is equal and opposite to the horizontal component of earth's magnetic field . )

A person , giving two equal loans, one at a rate of simple interest of 8% per annum and the other at a rate of simple interst of 6% per annum, earns a total interest of Rs756 after a period of time of 18 months. Find the total amount of money he has given as loan.

The weight of a wooden box made of wooden planks with the thickness of 5 cm along with its covering is 115·5 kg. But the weight of the box filled with rice is 880·5 kg. The length-and breadth of inner side of the box are 12 dcm and 8·5 dcm respectively and the weight of 1 cubic dcm rice is 1 ·5 kg. Determine the inner height of the box. Also determine the total expenditure to colour the outside of the box, if the rate is ₹ 1 ·50 per sq-dcm.

The external diameter of the base of a right circular cone - shaped wooden toy is 10 cm. The expenditure of colouring the total surface area on the outside of it at the rate of rs 0.07 per sq-cm is rs 19.80 Find the slant height of the toy.

A and B started a business in partnership by investing in the ratio of 7 : 9. After 3 months A withdraw 23 of its investment and after 4 months from the beginning B withdraw 33 1/3 of its investment. If a total earned profit is Rs. 10201 at the end of 9 months, find the share of each in profit.

A manufacturer produces two types of articles A and B. The production cost of an article A is Rs.250 and that of B is Rs.300. His total investment does not exceed Rs.20000 and he can store at most 100 articles. Formulate tha given data in the form of inequations and show graphically the region representing the solution of these inequations.