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Arithmetic: Simple Interest Test -5

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Question 1
A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs130. But if he had interchanged the amounts invested, he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest?
A
Rs 700
B
Rs 500
C
Rs 800
D
Rs 400
Question 1 Explanation: 
Amount invested at 12% = Rs A
Amount invested at 10% = Rs B
=> 130 =(A x 12 x1 )/100 +(B x 10 x1 )/100
=> 13000 =12A + 10B............................................................1
=> 134 =(A x 10 x1 )/100 +(B x 12 x1 )/100
=>13400 = 10A + 12B..............................................................2
Solving equations 1 and 2 we get
A = Rs 500
So the amount invested at the rate of 12% is Rs 500
Question 2
A money lender lent out Rs 25000 in two parts, one at 8% and the other at 8.5%. If the total annual income on the amount is Rs 2031.25, the money lent at 8% is?
A
Rs 12500
B
Rs 6250
C
Rs 10000
D
Rs 18750
Question 2 Explanation: 
Total money = Rs 25000
Let the amount which is lent is A at 8%
Therefore the other part which is at 8.5% = (25000 – A)
Therefore (A x 8 x 1)/100 + {(25000 – A) x 8.5 x 1}/100 = 2031.25
=> 8A + 212500 - 8.5A = 203125
=> A= Rs 18750
Question 3
The simple interest and the true discount on a certain sum amount to same percentage. The interest and true discount amount to Rs. 25 and Rs. 20 respectively. The sum is?
A
Rs 500
B
Rs 200
C
Rs 250
D
Rs 100
Question 3 Explanation: 
Let A be the amount of money
And R be the rate percentage
Then Simple Interest
= (A x R )/100 = 25
=> A x R = 2500...................................................1
For true discount (discount percentage calculated on the actual selling price)
=> [(A – 20) x R] /100 =20
=> (A x R -20R)/100 =20
=> AR – 20R = 2000..............................................2
From eq. 1 and 2 , we get
2500 – 20R = 2000
R = 25%
Now eq.1
A x 25 = 2500 =>A= 100
Question 4
A trader owes a merchant Rs. 10028 due in 1 yr; but the trader wants to settle the account after 3 months.  If the rate of interest is 12% per annum, how much cash should he pay?
A
Rs 9025
B
Rs 9200
C
Rs 9600
D
Rs 9300
Question 4 Explanation: 
Present value of money = v
Then   (v x 12)/100 + v = 10028
=> (0.12v + v) = 10028
=> (v) = 10028/1.12
Now this amount will become after 3 months
[{(10028/1.12) x 12 x 3}/(12 x 100)] + 10028/1.12
=> {(10028 x 3) / 1.12 x100} + 10028/1.12
=> (10028/103)/ 112 = 9222.17 = Rs 9200
Question 5
Sona invests an amount of Rs.9535 at the rate of 4% per annum, for how many years did she invest the amount to obtain the double her sum?
A
10 yr
B
25 yr
C
5 yr
D
4 yr
Question 5 Explanation: 
Let Sona invested for Y years
A sum will be double when interest is equal to principal
9535 = (9535 x 4 x Y)/100
4Y= 100
Y= 25 years
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