Question 1 1 / -0
Find the simple interest on Rs. 2000 at 6% per annum for 1 year and 7 months.
Solution
Principal = Rs. 2000
Rate of interest = 6%
Time = 1 year 7 months = 19 months =
Simple interest =
, where T is in years.
= Rs. 190
Question 2 1 / -0
Find the amount obtained on a sum of Rs. 1560 at the rate of 9
% per annum on simple interest for 6 months.
Solution
Principal = Rs. 1560
Rate of interest = Time = 6 months =
Amount = Principal + Interest = Rs. 1560 + Rs. 76.05 = Rs. 1636.05
Question 3 1 / -0
Sachin borrowed Rs. 1500 from Harbhajan Singh at 14% per annum simple interest. After 5 years, he gave Rs. 2100 and a watch to Harbhajan Singh to clear the account. Find the cost of the watch.
Solution
Principal amount Sachin borrowed = Rs. 1500
Rate of interest = 14%
Time = 5 years
= Rs. 1050
Amount = Rs. (1500 + 1050) = Rs. 2550
After 5 years, he gave Rs. 2100 and a watch.
Rs. 2550 = Rs. 2100 + Cost of watch
Cost of watch = Rs. 450
Question 4 1 / -0
Find the simple interest on Rs. 1400 at 9% per annum for the period from 13th March, 1999 to 17th June, 1999.
Solution
Principal = Rs. 1400
Rate of interest = 9% P.A.
Time = 13
th March to 17
th June
= 96 days
= Rs. 33.14
Question 5 1 / -0
Robin lent out Rs. 9 on the condition that the loan is payable in 10 months by 10 equal installments of Re. 1 each. Find the rate of interest per annum.
Question 6 1 / -0
A sum amounts to Rs. 576 after a certain period of time, when reckoned at 8% per annum. If the simple interest is Rs. 126, then find the time period.
Solution
Amount = Rs. 576
Simple interest = Rs. 126
Principal = 576 - 126 = Rs. 450
Rate of interest = 8% per annum
T =
Time =
years
Question 7 1 / -0
A certain sum gives Rs. 3840 as simple interest in 3 years at the rate of 10%. Find the amount received at the end of 3 years.
Solution
According to the question:
S.I =
P = Rs. 12,800
Total amount received at the end of 3 years = Rs. (12,800 + 3840) = Rs. 16,640
Question 8 1 / -0
A certain amount of money, when reckoned at simple interest of 9½% per annum, amounts to Rs. 1416 after 5 years. Find the amount of money.
Solution
Let principal (required amount of money) = Rs. x
Rate of interest =
=
%
A = Rs. 1416
T = 5 years
Interest =
Amount = Interest + Principal =
x = 960
Thus, principal = Rs. 960
Question 9 1 / -0
Divide an amount of Rs. 6000 into two parts so that the simple interest on the first part for 2 years at the rate of 6% p.a. is equal to the simple interest on the second part for 3 years at the rate of 8% p.a.
Solution
Let the first part be x.
So, the second part = 6000 - x
For the first part,
I =
I =
For the second part,
I = I
2 12x = 144000 - 24x
36x = 144000
x = 4000
Hence, the first part is Rs. 4000 and the second part is Rs. 2000.
Question 10 1 / -0
A sum of money amounts to Rs.744 in 2 years and Rs.816 in 3 years. Find the rate of interest.
Solution
Let the principal be Rs.x.
Rate = r%
= I
1 =
2
nd Condition
=
Subtracting (1) from (2)
A
1 - A
2 =
Substituting the value of r in equation (1)
744 = x +
744 = x + 144
x = 600
Substituting x = 600 .. (3)
r = 12%
Question 11 1 / -0
Dhiraj invests a part of Rs. 8000 at 4% p.a. and the remainder at 5% p.a. His annual income from the investments is Rs. 350. How much has he invested at each rate?
Solution
Let the part invested at 4% p.a. be x.
Remainder = 8000 - x
I
1 + I
2 = 350
- x + 40000 = 35000
x = Rs. 5000 and 8000 - x = Rs. 3000
Question 12 1 / -0
The simple interest on a certain sum of money for 2
years at 3
% per annum is Rs. 210. Find the sum.
Solution
SI = Rs. 210
P = Rs. x
R =
T =
2400 = x
Hence, the sum is Rs. 2400.
Question 13 1 / -0
Two equal sums are lent at 9% and 8% of simple interest. The former is recovered 6 months earlier than the latter and the amount in each case is Rs. 17,680. Find the time (in years) for which they are lent.
Solution
Let the principal be Rs. x.
R
1 = 9%
R
2 = 8%
Time = t months
And A
1 = A
2 t = 48 months
t = 4 years
4,
Question 14 1 / -0
The simple interest on a sum of money will be Rs. 600 after 10 years. If the principal is tripled after 5 years, what will be the total interest at the end of the tenth year?
Solution
Simple interest after 5 years = Rs. 300
Question 15 1 / -0
Two equal sums are lent for the same time at 6% and 5% of simple interest. The former is received 2 years earlier than the latter and the amount in each case is Rs. 2400. Find the sum.
Solution
Let the principal be Rs. x.
R
1 = 6%
R
2 = 5%
A
1 = A
2 6t
1 = 5t
2 6(t - 2) = 5t
6t - 12 = 5t
t = 12
t
1 = t - 2
t
1 = 10 years
Question 16 1 / -0
Find the compound interest on Rs. 480 at the rate of 16
% per annum for 2
years.
Solution
Principal = Rs. 480
Time = 2
A = P
t
=
=
For
,
Total amount =
= 735 - 480 = Rs. 255
Question 17 1 / -0
A sum of money doubles itself in 10 years at some compounded rate of interest. In how many years, will it be four times of itself at the same rate?
Solution
Let, Rate = R %
Principal = x
Amount = 2x
Amount =
2 =
When money is four times, the amount is 4x.
Now,
4 = 2
2 Time = 20 years
Question 18 1 / -0
Find the difference between the compound interests when compounded half yearly and compounded quarterly on Rs. 900 for 1 year at a rate of 20% per annum.
Solution
P = Rs. 900
Rate of interest = 20% p.a.
For half yearly, n = 2 and R = 10%
A = Rs.
= Rs.
= Rs. 121
9 = Rs. 1089
For quarterly, n = 4 and R =
A = Rs.
= Rs.
= Rs.
(when nt = 4)
= Rs.
= 1093.95
Difference in CI = Rs. 1093.95 - Rs. 1089 = Rs. 4.95
Question 19 1 / -0
If Rs. 450 amounts to Rs. 504 in 3 years, what will Rs. 615 amount to in 2½ years at the same rate of simple interest?
Solution
Principal = Rs. 450
Amount after 3 years = Rs. 504
SI =
A = SI + P
504 - 450 =
= r
r = 4%
= Rs. 61.5
Amount = P + SI
= Rs. 615 + 61.5
Rs. 676.50
Hence, Rs. 615 will amount to Rs. 676.50.
Question 20 1 / -0
The sum is invested at the simple interest payable annually. The interest in two successive years, starting from first year, was Rs. 500 and Rs. 540. Find the sum.
Solution
S.I. on Rs. 500 for 1 year = 540 - 500 = Rs. 40
Question 21 1 / -0
Nitish borrowed Rs. 900 at the rate of 4% p.a. and Rs. 1100 at the rate of 5% p.a. for the same duration. He had to pay Rs. 364 in all as simple interest. Find the time period
Solution
Principal = Rs. 900
Rate = 4% p.a.
T = t years
I
1 = 36t
For 2
nd principal,
P = Rs. 1100
R = 5% p.a.
T = t
I
2 = 55t
I
1 + I
2 = 36t + 55t
364 = 91t
4 years = t
Question 22 1 / -0
How much will the simple interest be given at the rate of 17% per annum for Rs. 5950 for 3½ years?
Solution
Smple interest = Rs. 5950
Time =
years =
years
Rate = 17% p.a.
x = 10000
Question 23 1 / -0
A sum of money becomes
of itself in 6 years at a certain rate of simple interest. Find the rate of interest.
Question 24 1 / -0
A sum of money at a compound interest doubles in one year. In how many years will it amount to 8 times itself?
Solution
Let the principal be x.
After one year, it is 2x.
Time = 3 years
Question 25 1 / -0
Nishit deposited a certain sum of money in a post office at simple interest of 10% p.a. for 4 years and deposited an equal amount in a fixed deposit in a bank at simple interest for 5½ years at 11% p.a. If the difference in the interest from the two sources is Rs. 563.75, find the sum deposited.
Solution
Let the money deposited in the post office be x.
R = 10% p.a.
T = 4 years
I
1 =
Money deposited in fixed deposit = x
R
2 = 11% p.a.
T = 5½ years
Difference in interest = Rs. 563.75
= Rs. 563.75
= Rs. 2750
Question 26 1 / -0
A car bought for Rs.13,350 depreciates each year by 12 ½%. In how many years will its value be reduced to Rs. 6000?
Solution
Using principal, and Amount and compound interest formula:
Principle = 13,350, Rate =
%
Amount = 6000
So, 6000 = 13,350
⇒ 6000 = 13,350
⇒
⇒
⇒ For n = 6,
So, n = 6
Question 27 1 / -0
Amit lends Rs.3500 to Meena at the rate of 10% per annum and Meena lends the sum to Rainu at the rate of 11.5% per annum. Find the gain of Meena in a period of 3 years.
Solution
Difference in interest = (11.5 - 10)% = 1.5%
Interest =
Interest
Question 28 1 / -0
A sum of Rs. 5,000 at compound interest becomes double in 5 years. What will be the amount in 20 years?
Solution
The amount of Rs. 5,000 gets doubled in 5 years.
Question 29 1 / -0
Nidhi deposited Rs.2500 on January 4, 1984 in Punjab National Bank at 7
% per annum. She withdrew the whole amount on May 30, 1984. What interest did the bank pay?
Solution
Principal = Rs.2500
Rate =
Time = 145
=
= Rs.74.86 = Rs.75 (approximately)
Question 30 1 / -0
At what rate of interest compounded yearly will Rs. 80,000 amount to Rs. 88,200 in 2 years?
Solution
A = Rs. 88,200
P = Rs. 80,000
T = 2 years
5% = R
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