Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.
16. A finance company claims to lend money at simple interest, but includes the interest every six months for calculating the principal. If they charge an interest of 8%, what is the effective rate of interest?
A. 8.5%
B. 8%
C. 8.16%
D. 9%
Answer
Explanation:
Consider a sum of Rs.100 Interest for the first 6 months = 100 * ½ *8/100
Rs.4
Interest for the next 6 months = 104 * ½ *8/100 => Rs.4.16
Interest at the end of 1 year = Rs.8.16
For a sum of Rs.100 Effective rate of interest = 8.16%
17. A sum of money becomes 7⁄5 of itself in 4 years at a certain rate of simple interest. The rate per annum is :
A. 9%
B. 10%
C. 11%
D. 12%
Answer
Explanation:
No explanation
18. 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. None of these
Answer
Explanation:
Let the sum be Rs. 100. Then,
S.I. for first 6 months = Rs.(100 x 10 x 1)/( 100 x 2 ) = Rs. 5
S.I. for last 6 months = Rs. (105 x 10 x 1)/( 100 x 2)= Rs. 5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 – 100) = 10.25%
19. A sum of Rs. 7700 is to be divided among three brothers Vikas, Vijay and Viraj in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 years respectively remains equal. The Share of Vikas is more than that of Viraj by
A. Rs.1200
B. Rs.1400
C. Rs.2200
D. Rs.2800
Answer
Explanation:
Let Vikas, Vijay and Viraj gets Rs.x, Rs.y and Rs.z respectively.
Simple Interest on x at 5% for 1 year= x×5×1100
Simple Interest on y at 5% for 2 year= y×5×2100
Simple Interest on z at 5% for 3 year= z×5×3100
5x=10y=15z
x=2y=3z
y=x/2 and z=x/3—(1)
x + y + z = 7700 (∵ the total amount is Rs.7700)
x+x/2+x/3=7700(∵substituted the values of y and z from equation 1)
11x/6=7700
x/6=7000
x=4200
z=x/3=4200/3=1400
i.e, Vikas gets Rs.4200 and Viraj gets Rs.1400
Share of Vikas is more than that of Viraj by (4200 – 1400) = 2800
20. A certain sum of money lent out at S.I. amounts to Rs. 690 in 3 years and Rs. 750 in 5 years. The sum lent is:
A. Rs. 400
B.Rs. 500
C. Rs. 450
D.Rs. 600
Answer
Explanation:
SI for 2 year = 750-690 = 60
SI for 3 year (60/2)*3 = 90
Principal = 690-90
21. An amount increases by 40% in 5 years at simple interest. By how much % does it increase in 2 years at the same rate on compound interest?
A. 21%
B. 17.28%
C. 16.64%
D. 13.31%
Answer
Explanation:
S.I = 0.4P = P*5*R/100
R=8%
A =P[1+(8/100)]^2
[1.08]^2
1.1664P
It increases by 16.64%
22. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
A. 3.6%
B. 4.5%
C. 5%
D. None of these
Answer
Explanation:
Let the original rate be R%. Then, new rate = (2R)%.
Note:
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. year(s).
(725 x R x 1)/100 + (362.50 x 2R x 1) / (100 x 3 ) = 33.50
(2175 + 725) R = 33.50 x 100 x 3
(2175 + 725) R = 10050
(2900)R = 10050
R = 10050/2900= 3.46
Original rate = 3.46%
23. Prabhat took a certain amount as a loan from a bank at the rate of 8% p.a. S.I. and gave the same amount to Ashish as a loan at the rate of 12% p.a. If at the end of 12 years, he made a profit of Rs. 320 in the deal, what was the original amount?
A.Rs. 2000
B.Rs. 666.67
C.Rs. 3000
D.None of these
Answer
Explanation:
Let amount is x x * 12 *12 / 100 – x * 8 * 12 / 100 = 320 hence x = 666.67
24. A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year.
A. Rs. 167.50
B. Rs. 150
C. Rs.225
D. Rs. 112.50
Answer
Explanation:
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT100=5000×4×2100=400
He also lends it at 61⁄4% p.a for 2 years
Simple interest that he gets = PRT100=5000×254×2100=625
His overall gain in 2 years = Rs.625 – Rs.400 = Rs.225
His overall gain in 1 year = 2252 = Rs.112.5
25. Ram and Shyam deposit an equal amount of money in a bank at simple interest. Ram deposits for a time thrice as long as Shyam at two-thirds of Shyam’s interest rate. Find the ratio of the interests received by Ram and Shyam.
A. 2:3
B. 2:1
C. 3:2
D. 1:2
Answer
Explanation:
Let the amount be Rs.P
Interest received by Shyam = P*T*R/100
Interest received by Ram =>[ P*3T*(2/3)R]/100
= 2PTR/100
Ram’s Interest: Shyam’s Interest = 2:1
26. Mr. Thomas 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
Answer
Explanation:
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 – x).
Then, (x x 14 x 2)/100 + ((13900 – x) x 11 x 2)/100 = 3508
28x – 22x = 350800 – (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = Rs. (13900 – 7500) = Rs. 6400.
27. If a sum of Rs. 9 is lent to be paid back in 10 equal monthly installments of re. 1 each, then the rate of interest is
A. 11.33%
B. 11%
C. 266.67%
D. 26.67%
Answer
Explanation:
No explanation
28. The rate of growth of population of a village has been compounding annually at a constant rate of 5%. If the present population of the village is 10000, find the population after two years.
A. 10500
B. 11025
C. 15000
D. 10250
Answer
Explanation:
The current population is taken as P.
Population after 2 years = 10000[((1+(5/100))²] =11025
29. I borrowed two equal amounts, one at 12% S.I. for 2 years and the other at 10% for 3 years respectively. If the difference in the interest was Rs. 1200 , find the total amount borrowed.
A. Rs.20000
B. Rs.30000
C. Rs.40000
D. Rs.50000
Answer
Explanation:
Let the amount borrowed be Rs. x
SI on the first amount = 12*2*x/100 = 24x/100
SI on the second amount = 10*3*x/100 = 30x/100
Difference in the interests = 6x/100 = 1200
On Solving, x=Rs.20000
Total amount =Rs.40000
30. A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
A. 17.5 lakhs
B. 21 lakhs
C. 15 lakhs
D. 20 lakhs
Answer
Explanation:
Let Rs. x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (3,500,000 – x).
The elder daughter’s money earns interest for (21 – 16) = 5 years @ 10% p.a simple interest
The younger daughter’s money earns interest for (21 – 8.5) = 12.5 years @ 10% p.a simple interest.
As the sum of money that each of the daughters get when they are 21 is the same,
x= 210000= 21 lakhs
