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Friday, 11 March 2016

Interest: The money paid by the borrower to the lender for the use of money is called Interest.
Principal: The sum lent is called principal.
Simple Interest =
PTR / 100
Where P = Principal R= Rate of interest per annum
T= Time period in years
Amount= Principal + Simple Interest
Amount=> A = P x $\frac{100+RT}{2}$

Solved Problems on Simple Interest:
1.    Find the simple interest on Rs 8000 for 4 years at 10% p.a rate of interest?
a)    Rs 3500      b)Rs 4000       c)Rs 2400    d)Rs 4800
Explanation :     Simple Interest =
PTR / 100
= 8000 X 5 X
10 / 100
= Rs 4000
2.    Find the simple interest on Rs 2400 for 8 years 4 months at 6% per annum rate of interest ?
a)Rs 750        b)Rs 800         c)Rs 600     d)Rs 1200
Explanation:
Time period is 8 years 4 months = 8
4 / 12
years =
25 / 3
years
Simple Interest =
PTR / 100
= 2400 x
25 / 3
x
6 / 100
=Rs 1200

3. What is the simple interest on Rs 8000 from August 6th to December 30th at 5% p.a rate of interest?
a)Rs 240      b)Rs 200      c)Rs 160     d)Rs 120
Explanation: Number of days from August 6th to December 30th = 146 days (  we don’t count the given day)
Simple Interest=
PTR / 100
= 8000 x
146 / 365
x
5 / 100
= Rs 160

4.    What is the simple interest on Rs  2400 for 9 months at 4 paisa per rupee per month?
a)Rs 864    B)Rs 800      c)Rs 432      d)Rs 216
Explanation: P = Rs 2400
Time Period T = 9 months =
9 / 12
years = ¾ year
Rate of interest =4 paisa per Rupee per month= 4% per month= 48% p.a
Simple Interest=
PTR / 100
= 2400 X $\frac{3}{4}$ X
48 / 100
= Rs 864

5.    At what rate of interest per annum, will Rs 5500 be obtained as simple interest on Rs 25000 for 2 years 9 months?
a)    10%         b)9%         c)8%      d)7%
Explanation: Given P= Rs 25000 and

Time period = 2 years 9 months= 2
9 / 12
=
11 / 4
years
Simple Interest=
PTR / 100
5500 = 25000 X
11 / 4
X
R / 100
R = 8 %

6.    A man borrowed Rs  10000 from a lender at 9% per annum rate of interest .Find the amount to be paid by the man after 2 years 6 months?
a)    Rs 12000       b)Rs 12500    c)Rs 12250    d)Rs 15000
Explanation:
Principal = Rs 10000           Rate of interest R = 9%
T= 2 years 6 months= 2 ½ years=
5 / 2
years
Simple Interest=
PTR / 100
= 10000 X
5 / 2
X
9 / 100
= Rs 2250
Amount= Prinipal + Simple interest = Rs 10000+ Rs 2250 = Rs 12250

Alternate Method:  To find simple interest, we have a direct formula
A= P
(100+RT) / 100
= 10000 $\frac{100+\frac{5}{2}\times9}{100}$
= Rs 12250
7.    Sharma deposited Rs 9000 in a financial institution at 8% per annum rate of interest for 3 years. For many years must Tripathi deposit Rs 5,400 at 10% per annum rate of interest in another financial institution, so that both of them get same simple interest?
a)    4 years         b)10 years     c)12 years     d)14 years
Explanation: The simple interest on Rs 9000 at 8% rate of interest for 3 years should be equal to the simple interest on Rs 5400 at 10% for unknown years.
9000 X 3 X
8 / 100
= 5400 X T x
10 / 100
Therefore T = 4 years
Tripathi should deposit for 4 years to get same interest as Sharma

8.    Mr Bhattacharyya lent Rs 3600 to Mr Tiwary for 3 years and Rs 6600 to Mr Mishra for 2 years and he received Rs 1200  as simple interest in all. Find the rate of interest per annum?
a)    4%               b)5%            c)6%            d)12%
Explanation:
SI on 3600 for 3 years + SI on Rs 6600 for 2 years = 1200
3600 x 3 x
R / 100
+ 6600 x 2 x
R / 100
= 1200
ð  108R +132R = 1200
ð  240R= 1200
ð  R= 5%
The rate of interest per annum is 5%

9.    The simple interest on a sum of money is $\frac{1}{25}$ th of the principal. If the rate of interest is 16%. Find the time period?
a)    1 month        b)2 months    c)3 months    d)4 months
Explanation: Simple interest is
1 / 25
of the principal => SI =
1 / 25
P

1 / 25
P= P x
16 / 100
x T=>T= $\frac{1}{4}$ years
Therefore, the time period is
1 / 4
th year = 3 months

10. The simple interest on a sum of money is    $\frac{4}{25}$ of the principal and the rate of interest is equal to the number of years . What is the rate of interest?
a)4%       b)8%            c)16%           d)18%
Explanation :
Simple interest is
4 / 25
th of the principal => SI =
4 / 25
P.

Rate of interest per annum is equal to number of years => R =T
SI =
PTR / 100

4 / 25
P = P X R X
R / 100
=>R2 =
400 / 25
=>R=
20 / 5
=4%

11. A sum was put at a simple interest at a certain rate of 4 years. Had it been put a 3% higher rate, it would have fetched Rs 720 more. Find the principal?
a)Rs 4500 b)Rs 5000      c)Rs 6000      d)Rs 7200
Explanation: Let  rate of interest be R and principal be P.
SI at R rate of interest=> SI = P X 4 x
(R+4) / 25

If the rate of interest is 4% more, then SI= P X 4 x
(R+4) / 25
The difference between these two simple interests is Rs 720
P X 4 x
(R+4) / 25
-  P X 4 x
(R+4) / 25
= 720
P X 4 X
4 / 25
= 960
Therefore P= Rs 6000
12. Mr Shastri invested certain sum of money at 7% p.a for 4 years. However he would get Rs 1040 more simple interest, if he invests the same sum of money at 6% for 9 years. Find the sum (principal)?
a)Rs 8000           b)Rs 6000      c)Rs 5000      d)Rs 4000
Explanation: The difference between the simple interest obtained in two cases is Rs 1040.
Let Principal be P .
(P X 9 X
6 / 100
) - (P X 4 X
7 / 100
) = 1040
ð   $\frac{54P}{100}$   - $\frac{26P}{100}$ = 1040
ð  $\frac{26P}{100}$ = Rs 1040
ð  P=Rs  4000

13 In how many years will a sum of money becomes 4 times at 5% p.a simple interest?
a) 40 years   b)50 years   c)60 years    d)25 years
Explanation: Sum of money becomes 4 times=> Amount= 4P
Amount= P+ SI =>Simple interest= 4P-P
SI = P T
R / 100
=> 3P= P X T X
5 / 100
ð  T= 60 years
14. A sum of money becomes 4 times in 9 years at simple interest. In how many years will it become 8 times of itself at the same rate?
a)    21 years        b)18 years     c)15 years     d)12 years
Explanation:A sum of money ( principal) P becomes 4 times => Amount= 4P
Simple interest obtained is 3P
To get simple interest 3P, it takes 9 years.
To get simple interest P, it takes
9 / 3
= 3 years
Now it has to become 8 times => The simple interest to be obtained is 7P
To get simple interest P, it take s 3 years
So to get 7P as simple interest, it takes   7 x 3 = 21 years

15. Mr Gupta purchased an Apple mobile, He paid 12000 in cash and promised to pay Rs 40,320 after 3 years. If the rate of interest is 4% p.a, what is the price of the Mobile at present?
a)Rs 40000   b)Rs 48000    c)Rs 50000    d)Rs 52000
Explanation: Rs 40,320 to be paid after 3 years is equal to P present.
Amount = P
(100+RT) / 100
ð  40320= P    x
(100+ 3 X 4) / 100
ð  P= 40320 x $\frac{100}{112}$   = Rs 36000
Price of the mobile at present= Rs 36000+ Rs 12000 = Rs 48000

16. A certain sum of money amounts to Rs 2400 in 3 years and Rs 2720 in 5 years. Find the principal?
a)    Rs 1920      b)Rs 2050    c)Rs 2140      d)Rs 2250
Explanation: We know that Amount= Principal + Simple Interest
Principal + SI for 5 years= Rs 2720     (i)
Prinipical + SI for 3 years= Rs 2400    --(ii)
(i)-(ii) gives the SI for 2 years = 320
Simple interest for one year = Rs
320 / 2
= 160
Given P+SI for 3 years= 2400
ð  P + 3 x 160 = 2400 =>P=2400-480=Rs 1920

17. A sum of money Rs 32000 is lent in two parts, one at the rate of 10% and another at 12% . If the annual interest received is Rs 3600. What is the amount lent at 12%?
a)Rs 15000    b)Rs 18000    c)Rs 20000    d)Rs 24000
ð  $\frac{10P}{100}$ + 32000X $\frac{12}{100}$ – $\frac{12P}{100}$= 3600
ð  $\frac{2P}{100}$ = 3840-3600