# Simple Interest - Aptitude Questions and Answers - RejinpaulPlacement

8.
The simple interest on a sum of money is 4/9 of the principal. Find the rate percent and time, if both are numerically equal? [S.S.C. 2000]
Answer: b) 6   2/3 % , 6   2/3 yrs

Solution:   Let sum = Rs. x.
Then, S.I. = Rs. 4x/9.

Let rate = R % and time = R years.

Then, (x * R * R)/100 = 4x/9
=> R^2 = 400/9 = 20/3 = 6 2/3.

Rate = 6 2/3 % and Time = 6 2/3 yrs = 6 yrs 8 months
9.
The simple interest on a certain sum of money for 2   1/2 years at 12 % per annum is Rs. 40 less than the simple interest on the same sum for 3   1/2 years at 10 % per annum. Find the sum.

Solution:   Let the sum be Rs. x.

Then, [(x * 10 * 7)/(100 * 2)] - [(x * 12 * 5)/(100 * 2)] = 40
=> (7x/20) - (3x/10) = 40
x = (40 * 20) = 800

Hence, the sum is Rs. 800
10.
A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2 % higher rate, it would have fetched Rs. 360 more. Find the sum.

Solution:   Let the sum = R and Original rate = R.

Then, [(P * (R+2) * 3)/100] - [(P * R * 3)/100] = 360.
=> 3PR + 6P - 3PR = 36000
=> 6P = 36000
=> P = 6000.

Hence, sum = Rs. 6000.
11.
What annual instalment will discharge a debt of Rs. 1092 due in 3 years at 12 % simple interest?

Solution:   Let each instalment be Rs. x.

Then, [ x + [(x * 12 * 1)/100)]] + [x + [(x * 12 * 2)/100]] + x = 1092
=> 28x/25 + 31x/25 + x = 1092
=> (28x + 31x + 25x) = (1092 * 25)
x = (1092 * 25)/84 = 325

Each instalment = Rs. 325
12.
A sum of Rs. 1550 is lent out into two parts, one at 8 % and another one at 6 %. If the total annual income is Rs. 106, find the money lent at each rate? [L.I.C.A.A.O. 2003]

Solution:   Let the sum lent at 8 % be Rs. x and that at 6% be Rs. (1550 - x)

[(x * 8 * 1)/100] + [[(1550 - x) * 6 * 1]/100] = 106 .
=> 8x + 9300 - 6x = 10600
=> 2x = 1300
=> x = 650
Money lent at 8% = Rs.650.

Money lent at 6% = Rs. (1550 - 650) = Rs. 900
13.
At the rate of 8   1/2% p.a. simple interest, a sum of Rs. 4800 will earn how much interest in 2 years 3 months?