# Simple Interest - Aptitude Questions and Answers - RejinpaulPlacement

50.
Simple interest on a certain sum at a certain annual rate of interest is 1/9 of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is:

Solution:   Let the sum = x. Then, S.I. = x/9.
Let rate = R% and time = R years.

[(x * R * R)/100] = x/9
=> R^2 = 100/9
=> R = 10/3 = 3   1/3.

Hence, rate = 3    1/3%.
51.
Simple interest on a certain amount is 9/16 of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is: [R.R.B. 2003]

Solution:   Let sum = x. Then, S.I = (9/16)x.
Let rate = R%, and time = R years

[(x * R * R)/100] = 9x/16
=> R^2 = 900/16
=> R = 30/4 = 7   1/2.

Hence, time = 7   1/2 years
52.
A lends Rs. 2500 to B and a certain sum to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then the sum lent to C is: [S.S.C. 2003]

Solution:   Let the sum lent to C be Rs. x.

Then, [(2500 * 7 * 4)/100] + [(x * 7 * 4)/100] = 1120
=> (7/25)x = (1120 - 700)
=> x = [(420 * 25)/7] = Rs. 1500.
53.
Two equal sums of money were lent at simple interest at 11% p.a. for 3   1/2 years and 4   1/2 years respectively. If the difference in interests for two period was Rs. 412.50, then each sum is:

Solution:   Let each sum be x.

Then, [(x * 11 * 9)/(100 * 2)] - [(x * 11 * 7)/(100 * 2)] = 412.50
=> (99x - 77x) = 82500
=> 22x = 82500
=> x = 3750
54.
If the simple interest on a certain sum for 15 months at 7   1/2% per annum exceeds the simple interest on the same sum for 8 months at 12   1/2% per annum by Rs. 32.50, then the sum (in Rs.) is:

Solution:   Let the sum be Rs. x.

Then, [x * (15/2) * (5/4) * (1/100)] - [x * (25/2) * (2/3) * (1/100)] = 32.50
=> (75x/8) - (25x/3) = 3250
=> 25x = (3250 * 24)
=> x = [(3250 * 24)/25] = 3120.
55.
A man invests a certain sum of money at 6% p.a. simple interest and another sum at 7% p.a. simple interest. His income from interest after 2 years was Rs. 354. One-fourth of the first sum is equal to one-fifth of the second sum. The total sum invested was:

Solution:   Let the sum be x and y.

[(x * 6 * 2)/100] + [(y * 7 * 2)/100] = 354 or 6x + 7y = 17700 ....... (i)
Also, x/4 = y/5 or 5x - 4y = 0 ........ (ii)

Solving (i) and (ii), we get : x = 1200 and y = 1500.

Total sum = Rs. 2700.
56.
A borrowed some money from B at 12% p.a. S.I. for 3 years. He then added some more money to the borrowed sum and lent it to C for the same period at 14% p.a. rate of interest. If A gains Rs. 93.90 in the whole transaction, how much money did he add from his side?