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17. The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is tripled after 5 years, what will be the total interest at the end of the tenth year?
a. Rs.600
b. Rs.900
c. Rs.1200
d. Data inadequate

Answer: C

Explanation:
Let, sum = Rs.x, Time = 10 years Then S.I = Rs.600,
Rate = $\left( {\displaystyle\frac{{100 \times 600}}{{x \times 10}}} \right)$ = $\left( {\displaystyle\frac{{6000}}{x}} \right)\% $ per annum
S.I. on Rs.x for Ist five years
= Rs. $\left( {x \times \displaystyle\frac{{6000}}{x} \times 5 \times \displaystyle\frac{1}{{100}}} \right)$= Rs.300
S.I on Rs.3x for next 5 years
= Rs.$\left( {3x \times \displaystyle\frac{{6000}}{x} \times 5 \times \displaystyle\frac{1}{{100}}} \right)$= Rs.900
Total interest = Rs.(300 + 900)=Rs.1200

Alternatively:
Simple interest is linear with time. So If the SI is 600 for 10 years, then for 5 years, we get 300. Now if principal is trebled after 5 years, we get 3 times of actual interest for the last 5 years. i.e., 900. So total interest is Rs.1200

18. A lent Rs.600 to B for 2 years and Rs.150 to C for 4 years and received all together from both Rs.90 as simple interest. The total interest is :
a. 4%
b. 5%
c. 10%
d. 12%

Answer: B

Explanation:
Let, rate = x% per annum. Then,
${\displaystyle\frac{{600 \times x \times 2}}{{100}} + \displaystyle\frac{{150 \times x \times 4}}{{100}} = 90}$
or 18x = 90 or x = 5

19. A certain sum of money at simple interest amounts to Rs.1260 in 2 years and to Rs.1350 in 5 years. The rate percent per annum is :
a. 2.5%
b. 3.75%
c. 5%
d. 7.5%

Answer: A

Explanation:
S.I for 3 years = Rs.(1350-1260)=Rs.90
S.I for 2 years = Rs.$\left( {\displaystyle\frac{{90}}{3} \times 2} \right)$= Rs.60
Sum = Rs.(1260-60) = Rs.1200
Rate = ${\displaystyle\frac{{100 \times 60}}{{1200 \times 2}} = 2.5\% }$

20. A sum of money at simple interest amounts to Rs.2240 in 2 years and Rs.2600 in 5 years. The sum is :
a. Rs.1880
b. Rs.2000
c. Rs.2120
d. Data inadequate

Answer: B

Explanation:
S.I for 3 years = Rs.(2600-2240)=Rs.360
S.I for 2 years = Rs.$\left( {\displaystyle\frac{{360}}{3} \times 2} \right)$=Rs.240
Sum = Rs.(2240-240)=Rs.2000

21. Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest rate is increased by 3% , it would amount to how much ?
a. Rs.1056
b. Rs.1112
c. Rs.1182
d. Rs.992

Answer: D

Explanation:
Principal = Rs.800, S.I = Rs.(920-800) = Rs.120 and Time = 3 years
Original rate = $\displaystyle\frac{{100 \times 120}}{{800 \times 3}} = 5\% $
New rate = 8%
Now, S.I = Rs. $\left( {\displaystyle\frac{{800 \times 8 \times 3}}{{100}}} \right)$=Rs.192
Amount = Rs.992

22. At a certain rate of simple interest, a certain sum doubles itself in 10 years. It will triple itself in :
a. 15 years
b. 20 years
c. 30 years
d. 12 years

Answer: B

Explanation:
Let principal = P, We got P interest on Principal P for 10 years.
Now to make it triple, we have to get 2P interest on P. So after 20 years we get the money tripled.

Alternative Method:
Principal = P, S.I = P and Time = 10 years
$ \Rightarrow SI = \dfrac{{P \times T \times R}}{{100}}$
$ \Rightarrow P = \dfrac{{P \times 10 \times R}}{{100}}$
$ \Rightarrow R = 10$
Now to make it triple, we have to get 2P interest.
$ \Rightarrow 2P = \dfrac{{P \times T \times 10}}{{100}}$$ \Rightarrow T = 20$

23. A sum of money will double itself in 6 years at simple interest with yearly rate of :
a. 10%
b. $16\displaystyle\frac{2}{3}$%
c. 8%
d. 16%

Answer: B

Explanation:
Let Principal = P, Then S.I = P
Rate = $\dfrac{{100 \times SI}}{{P \times R}}$ = $\dfrac{{100 \times P}}{{P \times 6}} = \dfrac{{100}}{6} = 16\dfrac{2}{3}\% $

24. The simple interest on a sum of money is $\displaystyle\frac{1}{9}$ of the principal and the number of years is equal to the rate percent per annum. The rate percent per annum is :
a. 3
b. $\displaystyle\frac{1}{3}$
c. $3\displaystyle\frac{1}{3}$
d. $\displaystyle\frac{3}{{10}}$

Answer: C

Explanation:
Let principal = P, Then, S.I = $\displaystyle\frac{P}{9}$
Let Rate = R% per annum and
Time = R years
Then, $\displaystyle\frac{P}{9}$=${\displaystyle\frac{{P \times R \times R}}{{100}}}$ or
${R^2}$ = $\displaystyle\frac{{100}}{9}$ or Rs. $\displaystyle\frac{{10}}{3}$=$3\displaystyle\frac{1}{3}\% $ per annum

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