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Arithmetic: Simple Interest Test -6

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Question 1
Sanjay borrowed a certain sum from Anil at a certain rate of simple interest for 2 yr. He lent this sum to Ram at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 4200 as compound interest but paid Rs. 4000 only as simple interest, find the rate of interest.
A
15%
B
20%
C
35%
D
10%
Question 1 Explanation: 
Let Sanjay borrowed Rs a
Rate be r % with time = 2 yr
Therefore 4000= (a x r x 2)/100
r x a = 200000                                               ... (i)
=> a {1 + r/100}2 = a + 4200
=> (ar2/ 10000) + (2ar/100) =4200
=> 20r + 4000 = 4200.................................... from (i)
=> r = 10%
Question 2
Two equal sums of money were invested, one at 4% and the other at 41/2. At the end of 7 yr, the simple interest received from the latter exceeded that received from the former by Rs. 31.50. Each sum was?
A
Rs 1000
B
Rs 500
C
Rs 750
D
Rs 900
Question 2 Explanation: 
Let each sum be Rs a, then
From the given condition
{(a x 4 ½ x7)/100} - {(a x 4 x7)/100} = 31.50
=> 7a/100 x ½ = 63/2
=> a = Rs 900
Question 3
If the difference between the simple and the compound interests on same principal amount at 20% for 3 yr is Rs. 48, then the principal amount must be?
A
Rs 650
B
Rs 600
C
Rs 375
D
Rs 400
Question 3 Explanation: 
Let the principle amount be Rs 100
Then Simple Interest will be = (100 x 20 x 3)/100 = Rs 60
And the compound interest on the money will be
= {100(1+ 20/100)3} – 100
= 100 x (6/5)3 – 100 =364/5
So the difference between two of them will be
(364/5) – 60 = 64/5
If he difference is 64/5 m then the principal is Rs. 100
And if the difference is Rs. 48
Then the principle is {(100 x 5)/64} x 48 = Rs. 375
Question 4
I derive an annual income of Rs. 688.25 from Rs. 10000 invested partly at 8% per annum and partly at 5% per annum simple interest. How much of my money is invested at 5%?
A
Rs. 3725
B
Rs. 4225
C
Rs. 4800
D
Rs. 5000
Question 4 Explanation: 
Let the money which is invested be m
And the rate at which it invested = 5% (given)
There from the question
{(m x 1 x 5)/100} + {(10000 – m) x 1 x 8}/100 = 688.25
=> 5m – 8m + 80000 = 68825
=> 3m = 11175
=> m= Rs. 3725
Question 5
What equal annual installment will discharge a debt of Rs. 2985 due in 6 years at 10% simple interest?
A
349
B
453
C
398
D
none
Question 5 Explanation: 
If each equal annual installment is Rs a, then
Amount of Rs a in 5 years + Amount of Rs a in 4 years + Amount of Rs a in 3 years + Amount of Rs a in 2 year + Amount of Rs a in 5 years = Rs 299250
Or [a + (a X 10 X 5/100)] + [a + (a X 10 X 4/100)] + [a + (a X 10 X 3/100)] + [a + (a X 10 X 2/100)]+ [a + (a X 10 X 1/100)] + a = 2985
150 a + 140 a + 130 a + 120 a + 110 a + 100 a = 2985 X 100
750 a = 2985 X 100
a = 2985 X 100/750 = Rs 398
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