1.6 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSArithmetic
- What number should be subtracted from each of the numbers 17, 25, 31, 47 so that the remainders are
in proportion. [Ans. 3]
Hints :17 x 31 xor 3
25 x 47 x− = − =
(^) − − (^)
- 10 years before, the ages of father and son was in the ratio 5 : 2; at present their total age is 90 years.
Find the present age of the son. [Ans. 30 years] - The ratio of work done by (x–1) men in (x+1) days to that of (x+2) men in (x–1) days is
9 : 10 , find the value of x.
Hints: (x 1)(x 1) 9 & etc.
(x 2)(x 1) 10
− + =
(^) + − [Ans. 8]
1.2 SIMPLE & COMPOUND INTEREST (Including Application of Annuity)
1.2.1 Simple Interest
The price to be paid for the use of a certain amount of money (called principal) for a certain period is
known as Interest. The interest is payable yearly, half-yearly, quarterly or monthly.
The sum of the principal and interest due at any time, is called the Amount at that time.
The rate of interest is the interest charged on one unit of principal for one year and is denoted by i. If the
principal is 100 then the interest charged for one year is usually called the amount of interest per annum, and is denoted by r ( = Pi). e.g. if the principal is 100 and the interest ` 3, then we say usually that the rate of interest is 3 percent per
annum (or r = 3 %)
Here i= 1003 =0.03(i.e. interest for 1 rupee for one year).
Simple interest is calculated always on the original principal for the total period for which the sum (principal)
is used.
Let P be the principal (original)
n be the number of years for which the principal is used
r be the rate of interest p.a.
I be the amount of interest
i be the rate of interest per unit (i.e. interest on Re. 1 for one year)]
Now I = P.i.n, where i= 100 r
Amount A = P + I = P + P. i. n = P (1+ i.n) i.e. A = P (1 + n .i)
Observation. So here we find four unknown A, P, i., n, out of which if any three are known, the fourth one
can be calculated.