Q1. Mr. Hamilton invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
a) Rs. 6400 b) Rs. 6500 c) Rs. 7200
d) Rs. 7500 e) None of these
Q2. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
a) 3.5 years b) 4 years c) 4.5 years
d) 5 years e) None of these
Q3. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
a) 3% b) 4% c) 5%
d) 6% e) None of these
Q4. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
a) 10% b) 10.25% c) 10.5%
d) Data inadequate e) None of these
Q5. Aastha lent Rs. 5000 to Bahubali for 2 years and Rs. 3000 to Chinky for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
a) 5% b) 7% c) 7 1/8%
d) 10% e) None of these
Q6. Aman took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
a) Rs. 2000 b) Rs. 10,000 c) Rs. 15,000
d) Rs. 20,000 e) None of these
Q7. 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
Q8. Akshay borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 ¼ pa for 2 years. Find his gain in the transaction per year.
a) Rs. 112.50 b) Rs. 125 c) Rs. 150
d) Rs. 150 d) Rs. 167.50
Q9. On a sum of money, the simple interest for 2 years is Rs.660, while the compound interest is Rs.696.30, the rate of interest being the same in both the cases. The rate of interest is :
a) 10% b) 10.5% c) 12%
d) Data inadequate e) None of these
Q10. Mr.Devilal Singh invested an amount of Rs.13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs.3508, what was the amount invested in Scheme B?
a) Rs.6400 b) Rs.6500 c) Rs.7200
d) Rs.7500 e) None of these
Q11. What should be the least number of years in which the simple interest on Rs.2600 at [6(2/3)]% will be an exact number of rupees?
a) 2 b) 3 c) 4
d) 5 e) None of these
Q12. An amount of Rs.1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second, 11% p.a. If the total interest at the end of one year is [9(3/4)]%, then the amount invested in each share was :
a) Rs.52,500, Rs.47,500 b) Rs.62,500, Rs.37,500
c) Rs.72,500, Rs.27,500 d) Rs.82,500, Rs.17.500 e) None of these
Q13. 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 moinths at [12 (1 / 2)]% per annum by Rs.32.50, then the sum (in Rs.) is :
a) Rs.3000 b) Rs.3060 c) Rs.3120
d) Rs.3250 e) None of these
Q14. A sum of money trebles itself in 15 years 6 months. In how many years would it double itself?
a) 6 years 3 months b) 7 years 9 months c) 8 years 3 months
d) 9 years 6 months e) None of these
Q15. Rambo took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If he paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
a) 3.6 b) 6 c) 18
d) Data inadequate e) None of these
Solutions
1. Option A
Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 ⎯ x)
Then, [ x × 14 × 2 / 100] ÷ [{(13,900 - x) × 11 × 2 } / 100] = 3508
28x ⎯ 22x = 350800 ⎯ (13900 × 22)
6x = 45000
x = 7500
So, sum invested in Scheme B = Rs. (13900 ⎯ 7500) = Rs.6400
2. Option B
Time = [100 × 81 / 450 × 4.5 ] years = 4 years
3. Option D
S.I. = Rs. (15500 ⎯ 12500) = Rs.3000
Rate = [ 100 × 3000 / 12500 × 4 ]% = 6%
4. Option B
Let the sum be Rs.100. Then,
S.I. for first 6 months = Rs. [100 × 10 × 1 / 100 × 2] = Rs.5
S.I. for last 6 months = Rs. [105 × 10 × 1 / 100 × 2] = Rs.5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs.110.25
So, effective rate = (110.25 ⎯ 100) = 10.25%
5. Option D
Let the rate be R% p.a.
Then, [ 500 × R × 2 / 100 ] + [300 × R × 4 / 100] = 2200
100R + 120R = 2200
R = [2200 / 220] = 10
So, rate = 10%
6. Option C
Principal = Rs. [ 100 × 5400 / 12 × 3] = Rs.15000
7. Option C
Let the principal be P and rate of interest be R%.
So, required ratio = [P × R × 6 / 100] / [P × R × 9 / 100] = 6PR / 9PR = 6 / 9 = 2 : 3
8. Option A
Gain in 2 years = Rs. [(5000 × 25 / 4 × 2 / 100 ) ⎯ (5000 × 4 × 2 / 100 )]
= Rs. (625 ⎯400)
= Rs.225
So, gain in 1 year = Rs. [225 / 2] = Rs.112.50
9. Option E
Difference in C.I. and S.I. for 2 years – Rs. (696.30 ⎯ 660) = Rs.36.30
S.I. for one year = Rs.330
10. Option A
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 ⎯x)
Then, [x × 14 × 2 / 100 ] + [(13,900 - x) × 11 × 2 / 100] = Rs.3508
28x ⎯ 22x = 350800 ⎯ (13900 × 22 )
6x = 45000
x = 7500
So, sum invested in Scheme B = Rs. (13900 ⎯ 7500) = Rs.6400
11. Option B
S.I. = Rs. [2600 × 20 / 3 × 1 / 100 × T] = Rs.[ 520 / 3 × T]
Which is an exact number of rupees when T = 3
12. Option B
Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 ⎯ x)
Then, [x × 9 × 1 / 100 ] + [ (100000 - x) × 11× 1 / 100 ] = [100000 × 39 / 4 × 1 / 100 ]
9x + 1100000 - 11x / 100 = 39000 / 4 = 9750
2x = (1100000 ⎯975000) = 125000
x = 62500
Sum invested at 9% = Rs.62500
Sum invested at 11% = Rs. (100000 ⎯62500) = Rs.37500
13. Option C
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
14. Option B
Let sum = x. Then, S.I. = 2x, Time = 15 (1/2) years = 31 / 2 years
So, rate = [ 100 × 2x / x × (31/2)]% = 400 / 31%
Now, sum = x, S.I. = x, Rate = 400 / 31%
So, time = 100 × x / x × (400/31) = 31 / 4 years = 7 years 9 months
15. Option B
Let rate = R% and time = R years
Then, [1200 × R × R / 100] = 432
12 r2 = 432
R2 = 36
R = 6
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