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Arithmetic: Simple Interest Test -1

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Question 1
If Rs. 1000 be invested at interest rate of 5% and the  interest be added to the principal after 10 yr, then the  number of years in which it will amount to Rs 2000 is ?
A
162/3 yr
B
161/4 yr
C
16 yr
D
11 yrr
Question 1 Explanation: 
First we calculate the SI for 10 years
SI for 10 years is
=> (1000 x 5 x 10)/100 = Rs 500
Now new principal is
P = Rs. 1500
A = Rs. 2000
SI = Rs. 500
SI = (P x R xT)/100
T = (500 x 100)/ 1500 x 5 = 162/3 yr
So, the total amount of Time is 10 +62/3 yr = 162/3 y
Question 2
A sum of Rs7700 is to be divided among three brothers Bharat, Rakshit and Maninder in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 yr respectively remains equal. The share of Bharat is more than that of Maninder by:
A
Rs 2800
B
Rs2500
C
Rs3000
D
Rs2700
Question 2 Explanation: 
Let the three of them get p, q, r amount respectively
So at the rate of 5%, they have
(p x 5 x1 )/100 =(q x 5 x2 )/100 =(r x 5 x3)/100
=>p = 2q =3r
=> p:q:r = 6 : 3: 2
So the required amount = {(6 -2)/(6+3+2)} x 7700 = Rs 2800
Question 3
Amit borrowed a certain sum of money for 2 yr at 8% per annum on simple interest and immediately lent it to Ravi but at compound interest and gained Rs 16.  What amount did Amit borrow?
A
Rs1600
B
Rs2500
C
Rs24000
D
Rs1800
Question 3 Explanation: 
Let the amount borrowed by Amit is A
Then, A [(1+8/100)2- 1] – (A x 8x2)/100 =16
=> 0.1664A - 0.16A = 16
=> A = (16/0.0064) = Rs. 2500.
Question 4
Anu owes Biresh Rs. 1120 payable 2 yr hence; Biresh owes Anu Rs.1081.50 payable 6 months. If they decide  to settle their accounts forthwith by making the payments of money due right now, and the rate of interest be 6% per annum,  then who should pay and how much?
A
Anu, Rs70
B
Biresh, Rs 50
C
Anu, Rs50
D
Biresh, Rs 70
Question 4 Explanation: 
Let the present amount for Anu be= A
= (1120 – A) = (A x 6 x 2)/100
=> A = 1000 (amount Anu owes to Biresh)
Let the present amount for Biresh be = B
=>1081.50 – B = (B x 6 x 1)/ (2 x100)
=> 108150 –100B = 3
=> B = Rs 1050 (Amount Biresh owes to Anu)
Therefore Biresh should pay Rs 50 to Anu
Question 5
Natasha invested a certain sum of money in a simple interest bond whose value grew to Rs.300 at the end of 3 yr and to Rs.400 at the end of another 5 yr. What was the rate of interest in which he invested his sum?
A
12%
B
12.5%
C
6.67%
D
8.33%
Question 5 Explanation: 
Let principle = P
Let rate of interest =R
Then,
(P x R x 3)/100 + P = 300........................................1
(P x R x 8)/100 + P = 400.........................................2
Subtracting eq. 1 from eq.2 we get
(P x R x 5)/100 = 100
P x R = 2000
Now from eq. 1
(2000 x 3)/100 + P = 300
=> P = 240
Therefore 240 x R = 2000
R = 8.33%
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