Simple Interest
Simple Interest
A. Simple interest at 6 % per annum means that interest per year per 100 is 6. And
after 1 year every 100 becomes 100 + 6 = 106,
after 2 years every 100 becomes 100 + 6 + 6 = 112,
after 3 years every 100 becomes 100 + 6 + 6 + 6 = 118, etc.
Simple interest for 100 for 3 years at 6% rate of interest
= 3 × 6
Simple interest for 100 for n years at 6% rate of interest
= n × 6
Simple interest for 100 for n years at r% rate of interest
= n × r
B. If 4 bananas cost rupees 30 then cost of 6 = (30/4) × 6 = 45.
If a == b then c == (b/a) × c = b × c/a = (b × c)/a.
C. Simple interest for the amount 100 for n years at r% rate of interest = n × r
Hence, Simple interest for the amount P for n years at
r% rate of interest = ((n × r) / 100 )× P
= (P× n × r) / 100
D. After n years the amount P becomes
P + simple interest for P for n years
1. A sum of money at simple rate of interest becomes Rs 2016 in 4 years and
Rs 2286 in 9 years. What is the principal amount?
1. Rs.1800 2. Rs. 1700 3. Rs. 1900 4. Rs.1850
By D., P + 9 years interest = 2286 and
P + 4 years interest = 2016. Hence
Simple interest for 5 years(= 9 - 4) = 2286 - 2016 = 270
Simple interest for 4 years = 270 × 4/5 = 216
The principal amount = 2016 - 216 = 1800 Ans. 1.
2. A sum of money doubles in 14 years. In how many years would it triple if the
rate of interest considered as simple?
1. 25 years 2. 28 years 3. 18 years 4. 23 years
Since the sum of money doubles in 14 years,
14 years simple interest = principal amount.
Amount triples in 14 + 14 = 28 years. Ans. 2.
3. A man has invested ⅓ of his retirement gratuity at 6 % simple interest, ¼ of his
gratuity at 7% and the rest at 8 % simple interest. If the annual return of these
investments is Rs. 7012.5, find the total amount of gratuity invested by the man.
1. 89000 2. 99000 3. 95000 4. 105000
Let 100 be the total gratuity. Then
annual return = ⅓ × 6 + ¼ × 7 + (1 - ⅓ - ¼) × 8
= (24 + 21 + 40) / 12 = 85 / 12
(since 1 - ⅓ - ¼ = 5 / 12)
So, 85 / 12 = = 100
7012.5 = = 7012.5 × 100 × 12 / 85
= 84150 × 100 / 85 = 990 × 100 = 99000
Total gratuity = 99000 Ans. 2.
Aliter : Let x × 100 be the total gratuity.
x × ⅓ × 6 + x × ¼ × 7 +(1 - ⅓ - ¼)x × 8 = 7012.5
24 x + 21 x + 40 x = 7012.5 × 12 = 84150
85x = 84150
x = 990
Total gratuity = 990 × 100 = 99000 Ans. 2.
4. An amount of Rs 8500 becomes 9500 in 3 years time at some simple rate of
interest. How much the amount of Rs 10200 will become in 5 years at the same
rate of simple interest?
1. Rs. 11800 2. Rs. 12000 3. Rs. 12200 4. Rs 12800
3 years interest for 8500 = 9500 - 8500 = 1000
8500 × 3 == 1000
5 years Interest for 10200 ( : 10200 × 5) == (1000/(8500 × 3))×10200×5
= (1000/(17 × 3)) × 102 = 2000
10200 becomes in 5 years 10200 + 2000 = 12200 Ans. 3.
5. A certain sum of money becomes Rs 1000 in 2 years and Rs 1100 in 4 years at
simple rate of interest. The interest rate per annum is
1. 4 3/7 % 2. 5 5/9 % 3. 7 4/7 % 4. 6 4/9 %
Simple interest for 2 years (= 4 - 2) = 1100 - 1000 = 100
Principal amount = 1000 - 100 = 900.
Simple interest for 1 year = 100/2 = 50
900 == 50
Interest rate ( : 100 == (50/900) × 100 = 50/9 = 5 5/9 % Ans. 2.
6. A certain principal amount in 2 years at some simple interest becomes Rs 10000
and the same principal amount at the same rate of simple interest becomes 11000
in 3 years. Find the principal and the rate of interest.
1. 9200 and 14 % 2. 8500 and 13.5 % 3. 9000 and 13 % 4. 8000 and 12.5 %
Interest for one (3 - 2) year = 11000 - 10000 = 1000
Interest for 2 years = 2000
Principal = 10000 - 2000 = 8000
Since there is only one answer choice 8000, it is not necessary to calculate the
rate of interest. Ans. 4.
For completion we find the rate of interest.
For 8000 interest for one year = 1000
Interest rate = (1000/8000) × 100 = 12.5 %
7. A man earns Rs 12,500 as simple interest at 5 % per annum in 5 years.
Find the principal amount deposited by the man in the bank.
1.Rs 50000 2. Rs 45000 3. Rs 40000 4. Rs 35000
5 years interest for Rs 100 = 5 × 5 = 25
For interest 25 principal = 100
For interest 12500 principal = (100/25) × 12500 = 50000
Ans. 1.
8. If the simple interest on a certain principal amount at 5% per annum for 5 years
is Rs 900 more than the simple Interest on the same principal amount for 4 years at
4% per annum, then find out the principal amount.
1.Rs 9000 2. Rs 10500 3. Rs 10000 4. Rs 12000
Let the principal amount be Rs. 100.
Then
simple interest at 5% for 5 years - simple interest at 4% for 4 years
= 5 × 5 - 4 × 4 = 25 - 16 = 9
For 9 principal = 100
For 900 principal = (100/9) × 900 = 10000
Aliter : Let the principal amount be Rs. x
Then simple interest at 5% for 5 years - simple interest at 4% for 4 years
= x × 5 × (5/100) - x × 4 × (4/100)
= (25 - 16)(x/100) = 9x/100
Given 9x/100 = 900
x = 100 × 100 = 10000
9. An amount deposited at 5% simple interest becomes Rs 1512 in 4 years.
How much the same amount will become in 2 ½ years at 10% simple interest
per annum?
1.Rs 1475 2. Rs 1575 3. Rs 1675 4. Rs 1875
We assume that the Principal amount = 100
100 + 5 × 4 = 120 == 1512
100 + 10 × 5/2 = 125 == (1512 / 120) × 125 = 63 × 25 = 1575
Ans. 2
Rs 100 at 4% in 4 years becomes 100 + 5 × 4 = 120
Principal amount = (100/120) × 1512 = 1260
Rs 100 at 10% in 2 ½ years becomes
100 + 10 × 5/2 = 125
Rs 1260 at 10% in 2 ½ years becomes
(125/100) × 1260 = 1575
Ans. 2.
10. Simple interest accrued on a certain sum of principal is Rs 1200 in 4 years at
the rate of 8% per annum. What would be the simple interest accrued for thrice that
principal at the rate of 6% per annum in 3 years?
1. 2150 2. 2050 3. 2025 4. 2100
4 × 8 == 1200
3 × 3 × 6 == (1200 / (4 × 8)) × 3 × 3 × 6 = 75 × 27 = 2025 Ans. 3.
Aliter : Let the principal amount be x. Then
x × 4 × 8/100 = 1200
x = 3750
3x × 3 × 6/100 = 3 × 3750 × 3 × 6/100 = 75 × 27 = 2025
11. Out of Rs. 7000, some amount was lent at 6% per annum and the remaining at
4% per annum. If the total simple interest from both the fractions in 5 years was
Rs.1600, find the sum lent at 6% per annum.
(1) Rs.5000 (2) Rs.4000 (3) Rs.3000 (4) Rs.2000
Interest for one year from both = 1600/5 = 320
If all the 7000 was lent at 4%,
interest for one year = 7000 × 4/100 = 280
The difference 320 - 280 = 40 is due to the amount lent at 6%,
which is lent at 6 - 4 = 2% more.
For the difference 2, the sum lent at 6% is 100.
2 == 100
40 == (100/2) × 40 = 2000
Sum lent at 6% = (100/2) × 40 = 2000
Aliter: If x is the sum lent at 6% then
interest from both = x × 6/100 + (7000 - x) × 4/100
Hence, x × 6/100 + (7000 - x) × 4/100 = 320
6x + 28000 - 4x = 32000
2x = 32000 - 28000 = 4000
x = 2000
12. A sum of Rs. 1,550 was lent partly at 5% and partly at 8% per annum at simple
interest. The total interest received after 3 years was Rs. 300. The ratio of the
money lent at 5% to that lent at 8% is
(a)5:8 (b)8:5 (c)16:15 (d)31:6
5 + 8, 31 + 6 do not divide 1550, but 16 + 15 divides. So, Ans. 16:15
Aliter : Total interest per year = 300/3 = 100
Let x be the amount lent at 5%. Then
x × 5/100 + (1550 - x) × 8/100 = Total interest per year = 100
5x + (1550 - x) × 8 = 100 × 100
3x = 2400
x = 800, hence the ratio is 800 : 750 :: 16 : 15
Aliter : Total interest per year = 300/3 = 100
If all the 1550 was lent at 5%,
interest for one year = 1550 × 5/100 = 77.50
The difference 100 - 77.50 = 22.50 is due to the amount lent at 8%,
which is lent at 8 - 5 = 3% more.
Sum lent at 8% = (100/3) × 22.50 = 100 × 7.50 = 750
Sum lent at 5% = 1550 - 750 = 800
Required ratio is 800 : 750 :: 16 : 15
13. A person invests a certain sum at 6% S.I. and another sum at 7% S.I.
Income from interest after 2 years is Rs.354. If one fourth of the first sum is the
one fifth of the second sum then the total sum invested is
a) 2500 b) 2600 c) 2700 d) 2800
14 First sum = 15 second sum
i.e. First sumSecond sum = 45
The total sum is a multiple of 4 + 5 = 9
From the answer choices given only 2700 is a multiple of 9.
Aliter : Interest for one year = 177,
hence 6x + 7y = 17700 and ¼ x = ⅕ y i.e. 5x = 4y.
Solving the 2 equations, x = 1200, y = 1500. Total = 1200 + 1500 = 2700.
Aliter : Interest for one year = 177
Since ¼ of first sum is ⅕ of the second, we assume that the amount invested
at 6% and 7% be 400 and 500 respectively.
Then the interest for one year = 4 × 6 + 5 × 7 = 59
For interest 59 total sum = 900
59 == 900
177 == 177 × 900/59 = 3 × 900 = 2700.
14. Rs. 800 becomes Rs. 956 in 3 years at a certain simple rate of interest. If the
rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?
(a)Rs. 1,020.80 (b)Rs. 1,025 (c)Rs. 1,052 (d)Rs. 1,080.20
Increased interest = 4/100 × 800 × 3 = 96
Amount by increased interest = 956 + 96 = 1052
Aliter : For 100 increased interest for 3 years = 3 × 4
= 12
For 800 increased interest for 3 years = 12 × 8
= 96
Amount by increased interest = 956 + 96 = 1052
15. A sum of Rs. 800 amounts to Rs. 920 in 3 years at a simple interest.
If the interest rate is increased by 3%. What would Rs. 800 amount to?
(a)950 (b)970 (c)992 (d)1000
Interest increase = 8 × 3 × 3 = 72,
Amount = 920 + 72 = 992
16. A sum was put at simple interest at a certain rate for 2 years. Had it been put
at a 3% higher rate, it would have fetched Rs. 300 more. Find the sum.
(a)Rs. 5,000 (b)Rs. 4,000 (c)Rs. 10,000 (d)Rs. 1,000
Higher interest fetched for one year = 300/2 = 150
Sum = 100/3 × 150 = 5000
(Since for 3 amount 100, for 150 = 100/3 × 150)
17. How much time will it take for an amount 2,000 to double at a simple interest
rate 8% (a)25 ½ years (b)10 ½ years (c)8 ½ years (d)12 ½ years
Amount will double when total interest = principal
For 100 if interest is 8 then year = 1
For 100 if interest is 100 then year = 1008 = 12 ½ years
18. Amala invests Rs. 6,000 in a bond which gives interest at 4% per annum during
the first year, 5% during the second year, 10% during the third year.
How much does she get at the end of the third year?
(a)Rs. 7,300 (b)7,007.2 (c)Rs. 7,200 (d)7,207.2
Amount at the end of first year = 4/100 × 6000 + 6000 = 240 + 6000 = 6240
Amount at the end of second year = 5/100 × 6240 + 6240 = 312 + 6240 = 6552
Amount at the end of third year = 10/100 × 6552 + 6552
= 655.20 + 6552 = 7207.20
19. A sum becomes 1.6 times of itself in five years at a simple rate of interest.
Find rate of interest per annum?
(a) 10% (b) 12.5% (c) 15% (d) 12% (e) 8.5%
Taking principal 100, 5 years interest = 160 - 100 = 60
Interest rate = one year interest for 100 = 605 = 12
20. The cost of a dining table is Rs. 8,400. A wants to buy it in 10 installments.
His E.M.I. is Rs. 875. Find the rate of interest?
(a)3% (b)5% (c)8% (d)10%
Total repayment = 10 × 875 = 8750
Interest for 10 months = 8750 - 8400 = 350.
Interest for 12 months = 350 + 70 = 420
Interest rate = (420/8400) × 100 = 5%
Aliter : Interest rate = (350/8400) × (12/10) × 100 = 5%
21. A man deposited Rs 1.0 lakh in his bank account and earned a profit of
Rs 25000 @ 5% simple interest per annum. Find out the time period for which the
money deposited by the man remained in the bank.
1. 3 years 2. 5 years 3. 4 years 4. 7 years
One year interest for 1 lakh = 100000 × (5 / 100) = 5000
Time = 25000 / 5000 = 5 years Ans. 2.
22. Find the simple interest on Rs. 6,750 for 219 days at 10% per annum.
(a)205 (b)305 (c)405 (d)415
= 10/100 × 219/365 × 6750 = 110 × 35 × 6750 = 3 × 135 = 405
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