Aptitude question and answer on Simple interest

In this section we are going to discuss about simple interest problems. Not just the overview of the topic, but also you are going to learn the important formulas on simple interest along with explanation which is easy to understand.

1
In how many years will a sum of money double itself at 4% per annum ?
A.    8 years
B.    16 years
C.    12 years
D.    25 years

Answer : D.  25 years

Explanation:
Let  Sum = x 
Then  S.I = x
\(\dot{..}\) Time = \({100 \times S.I \over Sum \times Rate}\)
             =\(\bigg({100 \times x \over x \times 4} \bigg)\)years
             = 25 years

2
A person borrowed Rs. 1500 at the rate of 5% per annum S.I. what amount will he pay to clear the debt after 4 years ?
A.    Rs. 2000
B.    Rs. 1880
C.    Rs. 1800
D.    Rs. 1600

Answer : C.  Rs. 1800

Explanation:
Amount = Rs. \(\Bigg( 1500+{1500 \times5 \times4 \over100}\Bigg)\)=Rs. 1800

3
Rajnish took a loan for 7 years at the rate of 6% p.a. S.I. If the total paid was Rs. 2100, the principal was
A.    2%
B.    5%
C.    8%
D.    10%

Answer : A.  2%

Explanation:
Rate=\( \Bigg( {100 \times 300 \over5000 \times3} \Bigg)\%=2\%\)

4
At a certain rate of simple interest, a certain sum doubles itself in 10 years. If will triple itself in 
A.    12 years
B.    15 years
C.    20 years
D.    30 years

Answer : C.  20 years

Explanation:
Let     sum  = x.
Then   S.I.  = x and time = 10 years
\(\dot{..}\) Rate = \(\Bigg( {100 \times x \over x \times 10} \Bigg) \%=10\%\)
Now , Sum = x, S.I.=2x , Rate = 10 %
\(\dot{..}\) Time = \(\Bigg( {100 \times 2x \over x \times 10} \Bigg) \)years
                = 20 years

5
The simple interest on Rs. 18200 from March 9, 2001 to May 21, 2001 at of \(7{1 \over 2}\) rate percent will be
A.    Rs. 290
B.    Rs. 273
C.    Rs. 288
D.    Rs. 225

Answer : B.   Rs. 273

Explanation:
March + April + May = 22+30+21
                              = 73 days
                              =\({73 \over 365}\) year
                              = \({1 \over 5}\) year
\(\dot{..}\)              Interest  = Rs. \(\Bigg(18200 \times{1 \over5} \times {15 \over 2 \times 100} \Bigg)\)
                              =Rs. 273

6
A certain sum of money lent out at S.I. amounts to Rs. 6900 in 3 years and Rs. 7500 in 5 years. The sum lent is
A.    Rs. 4000
B.    Rs. 4500
C.    Rs. 5000
D.    Rs. 6000

Answer : A.  Rs. 4000

Explanation:
S.I. for 2 years = Rs (7500-6900)
                      = Rs. 600
S.I for 3 years = Rs. \(\bigg( {600 \over 2} \times 3 \bigg)\)
                      =Rs. 900
\(\dot{..}\)     Principal = Rs. (6900-900)
                     = Rs. 6000



7
A Sum of money triples itself in 15 years 6 months. in how many years would it double itself ?
A.    6 years 3 months
B.    7 years 9 months
C.    8 years 3 months
D.    9 years 6 months

Answer : B.   7 years 9 months

Explanation:
Let sum = x.
Then 
S.I.=2x and Time = \(31 \over 2\)years
\(\dot{..}\) Rate = \(\Bigg({100 \times 2x \over x} \times{2 \over31} \Bigg)\%\)
           =\(\bigg({400 \over 31} \bigg)\%\)
Now,       Sum=x,    S.I.=x
and      Rate = \(\bigg({400 \over 31} \bigg)\%\)
\(\dot{..}\) Time = \(\Bigg({100 \times x \over x} \times{31 \over 400} \Bigg)\)year
            =7 years 9 months.

8
For how many years should Rs. 1200 be invested at 10% p.a. in order to earn the same simple interest as is earned by investing Rs. 1800 at 12% p.a. for 5 years ?
A.    9
B.    10
C.    12
D.    11

Answer : A.  9

Explanation:
S.I required = Rs. \(\Bigg({1800 \times 12 \times 5 \over 100} \Bigg)\)
                 = Rs. 1080
         Time = \(\Bigg({1800 \times 1080 \over 1200 \times10} \Bigg)\)years
                 = 9 years