A student purchased a pen for $ 100. At the end of 8 months, it was valued at $ 60. Assuming the monthly depreciation is of constant amount, find the monthly depreciation.

A manufacturer instals a machine at a cost of $ 3,000. At the end of 9 years, the machine has a value of $ 1200. Assuming the yearly depreciation to be a constant amount, find its price after 13 years

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation (d V(t))/(dt) =-k(T-t) , where k"">""0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is : (1) T^2-1/k (2) I-(k T^2)/2 (3) I-(k(T-t)^2)/2 (4) e^(-k T)

A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.

A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of all the offices taken together.

A finance company has offices located in every division, every district and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superintendent, two clerks, one typist and one peon. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendent Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix notation find The total number of posts of each kind in all the offices taken together,

A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

A wire of mass 9.8*10^(-3) kg per metre passes over a friction less pulley fixed on the top of an inclined friction less plane which makes an angle of 30^@ with the horizontal. Masses M_(1) and M_(2) are tied at the two end of the wire. The mass M_(1) rests on the plane and the mass M_(2) hangs vertically downward. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100ms^(-1) . Find the values of masses M_(1) and M_(2) . Take g= 9.8ms^(-2) .