Simple Interest & Compound Interest – Part 2

1) What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
a) 1 : 3
b) 1 : 4
c) 2 : 3
d) Data inadequate
e) None of these

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Answer c) 2 : 3
Let the principal be P and rate of interest be R%.
Required ratio = ( [P x R x 6 / 100] / [P x R x 9 / 100]) = 6PR / 9PR = 6 / 9 = 2 / 3
= 2 : 3.

2) A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
a) Rs. 35
b) Rs. 245
c) Rs. 350
d) Cannot be determined
e) None of these

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Answer d) Cannot be determined
We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.

3) A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
a) Rs. 112.50
b) Rs. 125
c) Rs. 150
d) Rs. 167.50

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Answer a) Rs. 112.50
Gain in 2 years
= Rs. (625 – 400)
= Rs. 225.
Gain in 1 year = Rs. 225 = Rs. 112.50

4) A sum of money lent out at simple interest amounts of Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
a) Rs. 500
b) Rs. 600
c) Rs. 700
d) Rs. 710
e) None of these

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Answer b) Rs. 600
Principal + SI for 2 years = Rs. 720 —–(1)
Principal + SI for 7 years = Rs. 1020 —-(2)
Subtracting equation (1) from (2) we get,
SI for 5 years
= Rs. (1020 -720) = Rs. 300
SI for 2 years = Rs. 300× 2/5= Rs. 120
Principal = Rs. 720- Rs. 120 = 600

5) In what time will Rs. 72 become Rs. 81 at 25/4% per annum simple interest?
a) 2 years
b) 3 years
c) 2 years 6 months
d) Can’t determine
e) None of these

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Answer a) 2 years
Interest = Rs. (81-72) = Rs. 9
Let the time be t years.
9 = (72×25×t)/(4×100)
t=(9×400)/(72×25)=2 years

6) The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ?
a) 5%
b)6%
c)7%
d)8%

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Answer a) 5%
S.I. = 1680, R = 4% T = 5 years
Principal = (100 *1680)/ (5*4) = 8400
So P = 8400
Rate = (100 *1680)/ (8400 * 4) = 5%

7) The interest on a certain deposit at 4.5% p.a. is Rs. 405 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?
a) Rs.50
b) Rs. 45
c) Rs.40.5
d) Rs. 48.5

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Answer b) Rs. 45
S.I. = Rs. 405 R = 4.5% T = 1 year
Principal = (100 *405)/(4.5*1) = Rs.9000
S.I at 5% interest = (9000*5*1)/100 = Rs.450
Difference in interest = 450 – 405 = Rs.45

8) Mr.Govind invested an amount of Rs.13900 divided in two different schemes S1 and S2 at the simple interst rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in two years was Rs.3508, what was the amount invested in Scheme S2?
a) Rs.6400
b) Rs.6500
c) Rs.7200
d) Rs.7500

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Answer a) Rs.6400
Let the sum invested in Scheme S1 be Rs.x and that in Scheme S2 be Rs.(13900-x).
Then, (x*14*2)/100 + ((13900-x)*11*2)/100 = 3508;
28x-22x= 3350800-(13900*22);
6x = 45000; x= 7500
So sum invested in Scheme S2 = Rs. (13900-7500) = Rs.6400

9) A sum of money was invested in a bank at 8% simple interest p.a. for 3 years. Instead had it been invested in mutual fund at 8.5% p.a. simple interest for 4 years, the earning would have been Rs.500 more. What is the sum invested?
a) Rs.4500
b) Rs.5000
c) Rs.3500
d) Rs. 5500

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Answer b) Rs.5000
Let the sum be Rs.x
S.I from the bank = x*8*3/100 = 34x/100Earnings in the form of interest from mutual fund = (x * 8.5 *4)/100
= 34x/100
Given that 34x/100 – 34x/100 = Rs.500 ; x = 5000
The sum invested = 5000

10) A person borrowed Rs.600 @ 3% per annum S.I and Rs.800 @ 4½ % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.246. The number of years, after which the borrowed sum is to be returned, is
a) 2 years
b) 3 years
c) 4 years
d) 5 years

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Answer c) 4 years
Let the time be x years. Then (600 *3* x)/100 + (800*9*x)/(2*100) = 24
18x+ 36x = 246 ; x = 246/54 = 4 years
Required time = 4 years

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