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 sum of 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years.

A machine costs 5,00,000. If its value depreciates 15% in the first year, 13 (1/2) % in the second year, 12% in the third year and so on. What will be its value at the end of 10 years, when all the percentages will be applied to the original cost? [Total depression =15 + 13(1/2) + 12+ ......10 terms S_(n) = 10/2[30-13.5] = 82.5% therefore after 10 years original cost = 100 - 82.5 = 17.5, i.e. 17.5% of 5,00,000.

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.

A manufacture produces three products x,y,z which he sells in two markets . Annual sales are indicated below : (a) If unit sale prices of x,yand z are Rs. 2.50, Rs. 1.50 and Rs. 1.00 , respectively, find the total revenue in each market with the help of matrix algebra. (b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise repectively .Find the gross profit.

Two parallel beams of light P and Q (separation d) containing radiations of wavelengts 4000Å and 5000 Å (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure the refractive index of the prism as a function of wavelength is given by the relation mu(lamda)=1.20+(b)/(lamda^(2)) where lamda is in Å and b is a positive constant. The value of b is such that the condition for total reflection at the face AC is just satisfied for one wavelength and is not satisfied for the other. A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper and the lower beams immediately after transmission from the face AC, are 4I and I respectively, find the resultant intensity at the focus.

A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15^(th) year since he deposited the amount and also calculate the total amount after 20 years.

A student performs an experiment to determine how the range of a ball depends on the velocity with which it is projected. The "range" is the distance between the points where the ball lends and from where it was projected, assuming it lands at the same height from which it was projected. It each trial, the student uses the same baseball, and launches it at the same angle. Table shows the experimental results. |{:("Trail","Launch speed" (m//s),"Range"(m)),(1,10,8),(2,20,31.8),(3,30,70.7),(4,40,122.5):}| Based on this data, the student then hypothesizes that the range, R, depends on the initial speed v_(0) according to the following equation : R=Cv_(0)^(n) , where C is a constant and n is another constant. Based on this data, the best guess for the value of n is :-

Manufacturer can sell x items at a price of rupees (5-(x)/(100)) each. The cost price of x items is Rs. ((x)/(5)+500) . Find the number of items he should sell to earn maximum prodit.

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs. 5 and that from a shade is Rs. 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit ?

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize , find the value of each of the prizes.