First Principles AI

Questions

Question 1
A sum of Rs.10400 is paid off in 40 instalments such that each instalment is Rs.10 more than the preceding instalment. Calculate the value of the first instalment.
Solution Theory
Question 2
An investor invests Rs. 150000 at an annual compound interest rate of 6% for 8 years. Find the total amount will he get after 8 years.
Solution Theory
Question 3
The population of a town is 4084101 at present and five years ago it was 3200000. Find its rate of increase if it increased geometrically.
Solution Theory
Question 4
Determine the total worth of a yearly Rs. 5000 investment after 20 years if the interest rate is 5% compounded annually.
Solution Theory
Question 5
A water tank has a leakage. Each week, the tank loses 5 gallons of water due to the leakage. Initially, the tank is full and contains 2000 gallons.
(i)
How many gallons are in the tank 20 weeks later?
(ii)
How many weeks until the tank is half-full?
(iii)
How many weeks until the tank is empty?
Solution Theory
Question 6
A drug company has manufactured 7 million doses of a vaccine to date. They promise additional production at a rate of 1.4 million doses/month over the next year.
(i)
How many doses of the vaccine, in total, will have been produced after a year?
(ii)
The general term $a_n$ describes the total number of doses of the vaccine produced. Describe the meaning of the variable $n$ in the context of this problem. Find the general term $a_n$ .
(iii)
Find the value of $a_{10}$ and interpret its meaning in words.
Solution Theory
Question 7
At a toll booth, the number of vehicles passing through during the first minute is 100. Due to road congestion, each minute only 80% of the vehicles from the previous minute manage to pass.
(i)
Represent the number of vehicles passing each minute as a sequence.
(ii)
Find the total number of vehicles that pass through in 15 minutes.
(iii)
What is the maximum number of vehicles that can pass in the long run (as time $t \to \infty$ )?
Solution Theory
Question 8
A sum of Rs. 5000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an A.P.? If so find the interest at the end of 20 years making use of this fact.
Solution Theory
Question 9
A machine is purchased for Rs.20,000. Depreciates at 6% per annum for the first four years and after that 8% per annum for the next six years. Depreciation being calculated on diminishing value. Find the value of the machine after a period of 10 years.
Solution Theory
Question 10
Two cars start together in the same direction from the same place. The first goes with uniform speed of 20 km/h. The second goes at a speed of 12 km/h in the first hour and increases the speed by 1 km/h each succeeding hour. After how many hours will the second car overtake the first car if both cars go non-stop?
Solution Theory
Question 11
150 workers were engaged to finish a piece of work in a certain number of days. Five workers dropped the second day, five more workers dropped the third day and so on. It takes 10 more days to finish the work now. Find the number of days in which the work was completed.
Solution Theory
Question 12
A radioactive product has a half life of 5 years. If the radioactivity level is 68 microcuries after 20 years. Determine the original level of radioactivity.
Solution Theory
Question 13
An object moving in a line is given an initial velocity of 4.5 m/s and a constant acceleration of 2.5 m/s². How long will it take the object to reach a velocity of 20 m/s?
Solution Theory
Question 14
In an integrated circuit with an initial current of 1080 mA, the temperature in the components decreases from 20% to 17% to 14%. Assuming that each temperature decrease is caused by a decrease in the initial current, what is the value of the current at fourth measurement?
Solution Theory
Question 15
Show that the amount of a certain sum of money at compound interest of $r\%$ per year for $n$ years form a G.P.
Solution Theory