Q1. If the simple interest on a certain sum of money is 4/25 of the sum and the rate per cent equals the number years, then the rate of interest per annum is:
(a) 2%
(b) 3%
(c) 4%
(d) None of these
Q2. If a certain sum of money borrowed at 5% per annum simple interest amounts to Rs. 1020 in 4 years, then the sum of money borrowed is:
(a) Rs. 850
(b) Rs. 925
(c) Rs. 750
(d) None of these
Q3. If Rs. 1000 be invested at interest rate of 5% and the interest be added to the principal every 10 years, then the number of years in which it will amount to Rs. 2000 is:
(a) 16 2/3 years
(b) 16 1/4 years
(c) 16 years
(d) None of these
Q4. Sumit lends Rs. 10000 for 2 years at 20% per annum simple interest. After 1 year, he receives Rs. 6000. How much will be he receive next year?
(a) Rs. 5900
(b) Rs. 6400
(c) Rs. 7200
(d) None of these
Q5. A sum of money doubles itself in 8 years. In how many years will it treble?
(a) 16 years
(b) 15 years
(c) 14 years
(d) None of these
Q6. 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, remains equal. The share of Vikas is more than that of Viraj by:
(a) Rs. 2800
(b) Rs. 2500
(c) Rs. 3000
(d) None of these
Q7. Mr Mani invested an amount of Rs. 12000 at a simple interest rate of 10% per annum and another amount at a simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 14% per annum. Find the total amount invested.
(a) Rs. 20000
(b) Rs. 20800
(c) Rs. 21000
(d) None of these
Q8. Brinda borrowed Rs. 1000 to build a hut. She pays 5% simple interest. She lets the hut to Ramu and receives a rent of Rs. 12 1/2 per month from Ramu. In how many years Brinda would clear off the debt?
(a) 10 years
(b) 10 1/4 years
(c) 10 1/2 years
(d) None of these
Q9. Manish borrowed a sum of Rs. 1150 from Anil at the simple rate of 6 per cent p.a. for 3 years. He then added some more money to the borrowed sum and lent it to Sunil for the same time at 9 per cent p.a. at simple interest. If Manish gains Rs. 274.95 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sunil?
(a) Rs. 1290
(b) Rs. 1785
(c) Rs. 1285
(d) Rs. 1200
Q10. The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is:
(a) 5%
(b) 6 2/3%
(c) 6%
(d) 7 1/5%
Solutions
S1. Ans.(c)
Sol.
Let the principal be Rs. x
Then the simple interest (I)=4/25 x.
Let the rate of interest p.a. be r%, then time (T) = r years
∴ R=(100 × I)/(P × T)⇒r=(100 × 4/25 x)/(x × r)
⇒ r2=400/25 or r=20/5=4%
S2. Ans.(a)
Sol.
We have, A = Rs. 1020
T = 4 years
R = 5% p.a.
Let the principal be Rs. x
Then interest (I) = A – P = 1020 – x
Therefore, by using formula,
P=(100 × I)/(R × T)
We have, x=(100×(1020 – x))/(5 × 4)
⇒ x = 5100 – 5x or 6x = 5100
Or, x=5100/6 = Rs. 850
∴ The sum of money borrowed = Rs. 850
S3. Ans.(a)
Sol.
The interest earned in 10 years on Rs. 1000 at 5% per annum
=(1000 × 5 × 10)/100 = Rs. 500
The principal now becomes = Rs. 1000 + Rs. 500 = Rs. 1500.
We now find the time in which Rs. 1500 becomes Rs. 2000 at 5% p.a.
P = Rs. 1500
A = Rs. 2000
I = A – P = 2000 – 1500 = Rs. 500, R = 5% p.a.
∴ Time (T) =(100 × I)/(R × P)=(100 × 500)/(5 × 1500)=6 2/3 years
∴ Total time =(10+6 2/3) years =16 2/3 years
S4. Ans.(c)
Sol.
Amount after 1 year = P(1+(R × T)/100)
=10000(1+(20 × 1)/100)
= Rs. 12000
After paying Rs. 6000, the remaining sum = Rs. 6000
∴ Amount obtained in the next year
=P(1+(R × T)/100)
= 6000 (1+(20 × 1)/100) = Rs. 7200
S5. Ans.(a)
Sol.
We have, n = 2, T = 8 years, m = 3
∴ Required Time (T)=((m – 1)/(n – 1))×T
=((3 – 1)/(2 – 1))×8 = 16 years
S6. Ans.(a)
Sol.
Hence T1=1, T2=2, T3=3
R1=R2=R3=5%
The shares of Vikas, Vijay and Viraj will be in the ratio
1/(R1T1 )∶1/(R2T2 )∶1/(R3T3)=1/(1×5):1/(2×5)∶1/(3×5)
=1/1∶1/2∶1/3=6∶3∶2
Sum of proportional = 6 + 3 + 2 = 11
∴ Share of Vikas =6/11×7700 = Rs. 4200
Share of Vijay =3/11×7700 = Rs. 2100
Share of Viraj =2/11×7700 = Rs. 1400
Therefore, Vikas’s share is 4200 – 1400 = Rs. 2800 more than that of Viraj.
S7. Ans.(a)
Sol.
Here P1 = Rs. 12000, R1 = 10%, P2 = ?, R2=20%, R = 14%
Therefore, using the formula
R=(P1 R1+ P2 R2)/(P1+ P2 )
We get 14=(12000 × 10 + P2 × 20)/(12000 + P2 )
Or, P2= Rs. 8000
∴ Total amount invested = Rs.(12000+8000) = Rs. 20000.
S8. Ans.(a)
Sol.
Simple interest paid by Brinda on Rs. 1000 for 1 year =(1000 × 5 × 1)/100 = Rs. 50
Rent received by Brinda from Ramu in 1 year
=12 1/2×12 = Rs. 150
∴ Net savings = Rs. 100
Thus, Brinda will clear the debt of Rs. 1000 in 10 years
S9. Ans.(b)
Sol.
Suppose Manish added Rs. x to the borrowed money
Then,
3 × (9 – 6)% of 1150 + (9 × 3)% of x = 274.95
⇒ 9% of 1150 + 27% of x = 274.95
⇒ x=(274.95 – 103.5)/27×100 = Rs. 635
∴ Required value = 635 + 1150 = Rs. 1785
S10. Ans.(b)
Sol.
Let the sum of money be P
I=(P×R×T)/100⇒4/9 P=(P×R×T)/100
∴R=√(400/9)=20/3=6 2/3%
