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9. The rate of interest on a sum of money is 4% per annum for the first 2 years, 6% per annum for the next 4 years and 8% per annum for the period beyond 6 years. If the simple interest occured by the sum for a total period of 9 years is Rs.1120, what is the sum?
a. Rs.1500
b. Rs.2000
c. Rs.2500
d. Rs.4000

Answer: B

Explanation:
Let, sum = Rs.x. Then
$\displaystyle\frac{{x \times 4 \times 2}}{{100}} + \displaystyle\frac{{x \times 6 \times 4}}{{100}} + \displaystyle\frac{{x \times 8 \times 3}}{{100}} = 1120$
56x = 112000 or x = $\displaystyle\frac{{112000}}{{56}} = 2000$

10. Two equal amounts of money are deposited in two banks, each at 15% per annum, for $3\displaystyle\frac{1}{2}$ and 5 years. If the difference between their interest is Rs.144, each sum is :
a. Rs.460
b. Rs.500
c. Rs.640
d. Rs.720

Answer: C

Explanation:
Let each sum be Rs.P. Then,
$\displaystyle\frac{{P \times 15 \times 5}}{{100}} - \displaystyle\frac{{P \times 15 \times 7}}{{100 \times 2}} = 144$
$\displaystyle\frac{{3P}}{4} - \displaystyle\frac{{21P}}{{40}} \Rightarrow \displaystyle\frac{{9P}}{{40}} = 144$
P = $\displaystyle\frac{{144 \times 40}}{9} = 640$

11. The difference between the interests received from two different banks on Rs.500 for 2 years, is Rs.2.50.The difference between their rates is :
a. 1%
b. 0.5%
c. 2.5%
d. 0.25%

Answer: D

Explanation:
Let the rates be x% and y% . Then,
$\displaystyle\frac{{500 \times x \times 2}}{{100}} - \displaystyle\frac{{500 \times y \times 2}}{{100}} = 2.5$
$ \Rightarrow $10(x-y)=2.5 or x-y = 0.25

12. A certain sum of money at simple interest amounts to Rs.1012 in $2\displaystyle\frac{1}{2}$years and to Rs.1067.20 in 4 years. The rate of interest per annum is :
a. 2.5%
b. 3%
c. 4%
d. 5%

Answer: C

Explanation:
S.I for 1$\displaystyle\frac{1}{2}$ years = Rs.(1067.20-1012) = Rs.55.20
S.I for $\displaystyle\frac{5}{2}$ years = Rs. $\left( {55.20 \times \displaystyle\frac{2}{3} \times \displaystyle\frac{5}{2}} \right)$ = Rs.92
Sum = Rs. (1012-92) = Rs.920
Hence, Rate = $\displaystyle\frac{{100 \times 92 \times 2}}{{920 \times 5}} = 4\% $

13. At simple interest, a sum doubles after 20 years. The rate of interest per annum is :
a. 5%
b. 10%
c. 12%
d. data inadequate

Answer: A

Explanation:
Let, sum = P. Then, to make the money double, we have to get simple interest P on Principal P and time = T years
$SI = \dfrac{{PTR}}{{100}}$
$ \Rightarrow 2P = \dfrac{{P \times 20 \times R}}{{100}}$
$ \Rightarrow R = 5$

14. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is :
a. Rs.4800
b. Rs.6000
c. Rs.8000
d. Data inadequate

Answer: D

Explanation:
Let, sum = P. Then, S.I = $\displaystyle\frac{1}{2}P$, Rate = 8% and time = 6 years
$\displaystyle\frac{P}{2}$ = $\displaystyle\frac{{P \times 8 \times 6}}{{100}}$
Thus, data is inadequate.

15. A sum of money becomes $\displaystyle\frac{8}{5}$ of itself in 5 years at a certain rate of interest. The rate percent per annum is :
a. 5%
b. 8%
c. 10%
d. 12%

Answer: D

Explanation:
Let, sum = Rs.x.
Then, amount = Rs.$\left( {\displaystyle\frac{{8x}}{5}} \right)$
S.I = Rs.$\left( {\displaystyle\frac{{8x}}{5} - x} \right) = Rs.\left( {\displaystyle\frac{{3x}}{5}} \right)$
Rate = $\displaystyle\frac{{100 \times SI}}{{P \times T}}$ = $\displaystyle\frac{{100 \times \displaystyle\frac{{3x}}{5}}}{{x \times 5}}\% = 12% $

16. In how many years will sum of money double itself at 12% per annum?
a. 6 years 9 months
b. 8 years 3 months
c. 7 years 6 months
d. 8 years 4 months

Answer: D

Explanation:
Let, principal = Rs.P. Then S.I = Rs. P, Rate - 12%
Time = $\displaystyle\frac{{100 \times SI}}{{P \times R}}$ = $\left( {\displaystyle\frac{{100 \times P}}{{P \times 12}}} \right)$ years = 8 years 4 months.

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