Q: If an investment can earn 4% compounded monthly, what amount must you invest now in order to accumulate $10,000 after 3 years?
Solution: i=j/m PV = FV (1+ i)^-n
Q: Give an investment of $13200,compound amount of $22680.06 invested for 8 years,what is the interest rate if interest rate is compounded anually?
Solution: M = p(1+i)^n
Q: 15 semiannual payments are made into a sinking fund at 7% compounded semiannually so that $4850 will be present. Find the amount of each payment rounded to the nearest cent
Solution: R=S[i/(1+i)^n-1]
Q: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Solution: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.Q: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Solution: Let number of balls = (6 + 8) = 14. Number of white balls = 8. P (drawing a white ball) = 8 /14 = 4/7.
Q: I forgot the last digit of a 7-digit telephone number. If 1 randomly dials the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?
Solution: It is given that the last three digits are randomly dialed. then each of the digits can be selected out of 10 digits in 10 ways. Hence required probability =(1/10)3 = 1/1000
Q: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
Solution: On 31st December, 2005, it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days. On 31st December 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.
Q: How many years have 29 days in February from 2001 to 2100.
Solution: The 100th year is not a leap year. So 24 February’s has 29 days
Q: The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
Solution: Let the numbers be x and 4x. Then, x×4x=84×21 ⇔ x2=84×214⇔ x=21 Hence Larger Number = 4x = 84
Q: A rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?
Solution: 3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters=525 cm = 5 × 5 × 3 × 7 Hence common factors are 3 and 7 Hence LCM = 3 × 7 = 21 Hence largest size of square tiles that can be paved exactly with square tiles is 21 cm.
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