SIMPLE INTERST SET 1

 

 Simple Interest Set 1:

A portion of $6600 is invested at a 5% annual return, while the remainder is invested at a 3% annual return. If the annual income from the portion earning a 5% return is twice that of the other portion, what is the total income from the two investments after one year?
A.200
B.270
C.250
D.280
E.none of these

Answer- B (270)
Explanation – 5x + 3y = z (total)
x + y = 6600
5x= 2(3y) [ condition given]
5x – 6y = 0
x + y = 6600
5x -6y = 0
Subtract both equations and you get x = 3600 so y = 3000
3600*.05 = 180
3000*.03 = 90
z (total) = 270

If the simple interest on a certain sum of money is 4/25th of the sum and the rate percent equals the number of years, then the rate of interest per annum is:
A.2%
B.4%
C.8%
D.10%
E.None of these

Answer – B (4%)
Explanation – let principal =x then SI= 4/25 x
let rate be ” r” then time =r years
SI= PXRXT /100
put all here all will cut and we left with
r ^2 =400/25 = 4%

An automobile financier claims to be lending money at the 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.10.10%
D.10.80%
E.None of these

Answer – B (10.25%)
Explanation –
Let the sum be Rs. 100. Then,
S.I. for first 6 months = Rs. [100 x 10 x 1] / [100×2]= 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%.

The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rate of interest is:
A.0.20%
B.0.30%
C.0.50%
D.0.80%
E.None of these

Answer-B (0.30%)
SI=PXRXT/100 so,SI( 1) – SI (2)
[1500 x R1 x 3] /100 – [1500 x R2 x 3] /100 =13.5
4500 (R1 – R2) = 1350
R1 – R2 =1350/4500=0.30%

Nishu 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.6400
B.6500
C.7200
D.7500
E.None of these

Answer – A (6400)
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.

The difference between the Simple Interest and Compound Interest on a certain sum for 2 years at 15% Interest is Rs. 90. Find the Principal?
A.2500
B.3000
C.3500
D.4000
E.None of these

Answer – D (4000)
Explanation –
Difference between the compound interest and simple interest for 2 years = D= p(r/100)^2
P= Dx(100 /R)^2 = 90x100x100 /15×15=4000

If simple interest on a certain sum of money for 4 years at 5% per annum is same as the simple interest on Rs. 560 for 10 years at the rate of 4% per annum then the sum of money is:
A.1180
B.1120
C.1200
D.1250
E.None of these

Answer – B (1120)
Explanation – SI = PXRXT/100
make equation for both,and equate

A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much?
A.780
B.992
C.848
D.700
E.None of these

Answer – B (992)
Explanation –
S.I = Rs. (920 – 800) = Rs. 120; P = Rs. 800, T = 3 yrs
use SI=Px R x T/100 so, R = Si x 100 /Px t = ( 100 X 120 ) / 800 X 3 = 5%
New rate = (5 + 3) % = 8%
New S.I. = Rs. (800 X 8 X 3)/100 == Rs. 192.
New amount = Rs. (800 + 192) = Rs. 992

David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
A.Rs 5000
B.Rs 6500
C.Rs 8000
D.Rs 10000
E.None of these

Answer – A (Rs 5000)
Explanation:-Let x, y and z be the amounts invested in schemes A, B and C respectively. Then,
add individual interest to get total using Si= pxrxt/100
[x x 10 x 1]/100 + [y x 12 x 1]/100 + [z x 15 x 1]/100 = 3200
10x + 12y + 15z = 320000…. (i)Now, z = 240% of y =(12/5)y……… (ii)And, z = 150% of x =(3/2)x so,x=(2/3 )z = (2/3) x value of z from ii
x= (2/3) x (12/5) y = (8/5)y………..(iii)
From (i), (ii) and (iii), we have :
16y + 12y + 36y = 320000
64y = 320000
y = 5000
Sum invested in Scheme B = Rs. 5000

A certain sum is invested for T years. It amounts to Rs. 400 at 10% per annum. But when invested at 4% per annum, it amounts to Rs. 200. Find the time (T)?
A.39 years
B.41 years
C.45 years
D.50 years
E.None of these

Answer – D (50 years)
Explanation –
We have, A1 = Rs. 400, A2 = Rs. 200, R1 = 10%, R2 = 4%
Time (T) = [A1 – A2] x 100 divide by A2R1 – A1R2
= [400 – 200]x 100 divide by [200 x 10 – 400 x 4]= 20000/400 = 50 Years.