MCQ 11 Mark
The simple interest on a certain sum is $\frac{16}{25}$ of the sum. If the rate percent per annum and the time are numerically equal, then the rate percent is:
AnswerLet the sum $(P)$ be $Rs. x$
Then, the simple interest (I) $=\text{Rs.}\frac{16}{25}\text{x}$
Also,
Rate $(R) = R\%$
Time $(T) = R$ years ($\because$ the rate percent per annum and the time are numerically equal)
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$\Rightarrow\text{R}=\frac{100\ \times\ \text{I}}{\text{P}\ \times\ \text{T}}$
$\Rightarrow\text{R}=\frac{100\ \times\ \frac{16}{25}\text{x}}{\text{x}\ \times\ \text{R}}$
$\Rightarrow\text{R}\ \times \text{R}=\frac{{64\text{x}}}{\text{x}}$
$\Rightarrow\text{R}^2=8^2$
$\Rightarrow\text{R}=8\%$
Hence, the correct option is $(a).$
View full question & answer→MCQ 21 Mark
The difference between the interest obtained for $Rs. 1000$ at $12\%$ per annum for $3$ years and that for $Rs. 1500$ at $8\%$ per annum for $1\frac{1}{2}$ years is:
- A
$Rs. 360$
- B
$Rs. 300$
- ✓
$Rs. 180$
- D
$Rs. 200$
AnswerCorrect option: C. $Rs. 180$
It is given that,
$\operatorname{Sum}\left(P_1\right)= Rs. 1000$
Rate $\left(R_1\right)=12 \%$
Time $\left(T_1\right)=3$ years
$\mathrm{I}_1=\frac{\mathrm{P}_1 \times \mathrm{R}_1 \times \mathrm{T}_1}{100}$
$=\frac{1000 \times 12 \times 3}{100}$
$=$ Rs. $360 \ldots (i)$
Sum $\left(P_2\right)= Rs. 1500$
Rate $\left(R_2\right)=8 \%$
Time $\left(T_2\right)=1 \frac{1}{2}$ year $=\frac{3}{2}$ year
$\mathrm{I}_2=\frac{\mathrm{P}_2 \times \mathrm{R}_2 \times \mathrm{T}_2}{100}$
$=\frac{1500 \times 8 \times 3}{100 \times 2}$
$=$ Rs. $180 \ldots (ii)$
Subtracting $(ii)$ from $(i),$ we get
$I_2-I_1=$ Rs. $360- Rs. 180$
$=Rs. 180$
Hence, the correct option is $(c).$
View full question & answer→MCQ 31 Mark
If a sum of $Rs. 3000$ is lent out at $3 \%$ per annum for $20$ years under simple interest, then the amount at the end of $20^{\text {th }}$ year is:
- A
$Rs. 1800$
- B
$Rs. 1080$
- C
$Rs. 3600$
- ✓
$Rs. 4800$
AnswerCorrect option: D. $Rs. 4800$
It is given that,
Sum $(P) = Rs. 3000$
Rate $(R) = 3\%$
Time $(T) = 20$ years
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{3000\ \times\ 3\ \times\ 20}{100}$
$=\text{Rs. }1800$
Amount $= I + P = Rs. 1800 + Rs. 3000 = Rs. 4800$
Hence, the correct option is $(c).$
View full question & answer→MCQ 41 Mark
At what rate percent per annum simple interest will a sum double itself in $10$ years$?$
AnswerAmount $= 2$ times the sum $= 2P$
Simple interest $(I) =$ Amount $-$ Sum $= 2P - P = P$
Let the sum $(P)$ be $x.$
Then, simple interest $(I) = x$
Rate $(R) = R\%$
Time $(T) = 10$ years
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$\Rightarrow\text{R}=\frac{100\ \times\ \text{I}}{\text{P }\times\text{ T}}$
$=\frac{100\ \times\text{ x}}{\text{x } \times\ 10}$
$=10\%$
Hence, the correct option is $(b).$
View full question & answer→MCQ 51 Mark
If interest on $Rs. x$ for $2$ years at $R\%$ per annum is $Rs. 80,$ the interest on $Rs. 2 x$ for one year at $R\%$ per annum is:
- A
$Rs. 160$
- B
$Rs. 40$
- ✓
$Rs. 80$
- D
$Rs. 120$
AnswerCorrect option: C. $Rs. 80$
It is given that,
$\text { Sum }\left(P_1\right)=\text { Rs. } x$
$\text { Rate }\left(R_1\right)=R \%$
$\text { Time }\left(T_1\right)=2 \text { years }$
$\text { Interest }\left(I_1\right)=\text { Rs. } 80$
$I_1=\frac{P_1 \times R_1 \times T_1}{100}$
$\Rightarrow 80=\frac{x \times R \times 2}{100}$
$\Rightarrow \frac{2 R x}{100}=80 \ldots(i)$
Now,
$\operatorname{Sum}\left(P_2\right)=\text { Rs. } 2 x$
Rate $\left(R_2\right)=R \%$
Time $\left(T_2\right)=1$ year
$\mathrm{I}_2=\frac{\mathrm{P}_2 \times \mathrm{R}_2 \times \mathrm{T}_2}{100}$
$=\frac{2 \mathrm{x} \times \mathrm{R} \times 1}{100}$
$=\frac{2 \mathrm{Rx}}{100}$
$=80[\text { From }(\mathrm{i})]$
Therefore, $\mathrm{I}_2=$ Rs. 80
Hence, the correct option is $(c).$
View full question & answer→MCQ 61 Mark
The simple interest at $R\%$ per annum for $n$ years will be $Rs. n$ on a sum of:
AnswerCorrect option: C. $\text{Rs.}\frac{100}{\text{R}}$
It is given that,
Simple interest $(I) = Rs. n$
Rate $(R) = R\%$
Time $(T) = n$ years
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$\Rightarrow\text{P}=\frac{100\ \times\ \text{I}}{\text{R}\ \times\ \text{T}}$
$\Rightarrow\text{P}=\frac{100\ \times\ \text{n}}{\text{R}\ \times\ \text{n}}$
$\Rightarrow\text{P}=\frac{100}{\text{R}}$
Hence, the correct option is $(c).$
View full question & answer→MCQ 71 Mark
At which rate percent per annum simple interest will a sum triple itself in $16$ years$?$
AnswerAmount $= 3$ times the sum $= 3P$
Simple interest $(I) =$ Amount $-$ Sum $= 3P - P = 2P$
Let the sum $(P)$ be $x.$
Then, simple interest $(I) = 2x$
Rate $(R) = R\%$
Time $(T) = 16$ years
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$\Rightarrow\text{R}=\frac{100\ \times\ \text{I}}{\text{P}\ \times\ \text{T}}$
$\Rightarrow\text{R}=\frac{100\ \times\ 2\text{x}}{\text{x}\ \times\ 16}$
$\Rightarrow\text{R}=12.5\%$
Hence, the correct option is $(d).$
View full question & answer→MCQ 81 Mark
In what time will a sum of $Rs. 8000$ amount to $Rs. 8360$ at $6\%$ per annum simple interest$?$
AnswerCorrect option: B. $9\text{ month}$
It is given that,
Amount $= Rs. 8360$
Sum $= Rs. 8000$
Simple interest $(I) =$ Amount $-$ Sum $= Rs. 8360 - Rs. 8000 = Rs. 360$
Also,
Rate $(R) = 6\%$
Time $(T) = T$ years
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$\Rightarrow\text{T}=\frac{100\ \times\ \text{I}}{\text{P }\times\text{ R}}$
$=\frac{100\ \times\ 360}{8000\ \times\ 6}$
$=\frac{3}{4}\text{ years}$
$=\frac{3}{4}\text{ years}\times\text{12 month}$
$=\text{9 month}$
Hence, the correct option is $(b)$.
View full question & answer→MCQ 91 Mark
If $a, b$ and $c$ are three sums of money such that $b$ is the simple interest on $a$ and $c$ is the simple interest on $b$ for the same time and same rate. Which of the following is correct$?$
- A
$a b c=1$
- B
$c^2=a b$
- C
$b^2=ac$
- ✓
$a^2=b c$
AnswerCorrect option: D. $a^2=b c$
It is given that,
Simple interest $\left(\mathrm{I}_1\right)=\mathrm{b}$
$\operatorname{Sum}\left(P_1\right)=a$
Rate $\left(R_1\right)=R \%$
Time $\left(T_1\right)=T$ years
$\mathrm{I}_1=\frac{\mathbf{P}_1 \times \mathbf{R}_1 \times \mathbf{T}_1}{100}$
$\Rightarrow \mathrm{b}=\frac{\mathrm{a} \times \mathrm{R} \times \mathrm{T}}{100}$
$\Rightarrow \mathrm{R} \times \mathrm{T}=\frac{100 \mathrm{~b}}{\mathrm{a}} \ldots (i)$
Also,
Simple interest $\left(\mathrm{I}_2\right)=\mathrm{C}$
$\operatorname{Sum}\left(P_2\right)=b$
Rate $\left(R_2\right)=R \%$
Time $\left(T_2\right)=T$ years
Now,
$\mathrm{I}_2=\frac{\mathrm{P}_2 \times \mathrm{R}_2 \times \mathrm{T}_2}{100}$
$\Rightarrow \mathrm{c}=\frac{\mathrm{b} \times \mathrm{R} \times \mathrm{T}}{100}$
$\Rightarrow \mathrm{R} \times \mathrm{T}=\frac{100 \mathrm{c}}{\mathrm{b}} \ldots (ii)$
On equating (i) and (ii), we get
$\frac{100 \mathrm{~b}}{\mathrm{a}}=\frac{100 \mathrm{c}}{\mathrm{~b}}$
$\Rightarrow \mathrm{~b}^2=\mathrm{ac}$
Hence, the correct option is $(d).$
View full question & answer→MCQ 101 Mark
The amount on $Rs. 25000$ at $8\%$ per annum for $6$ years under simple interest is:
- A
$Rs. 35000$
- ✓
$Rs. 37000$
- C
$Rs. 45000$
- D
$Rs. 47000$
AnswerCorrect option: B. $Rs. 37000$
It is given that,
Sum $(P) = Rs. 25000$
Rate $(R) = 8\%$
Time $(T) = 6$ years
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{25000\ \times\ 8\ \times\ 6}{100}$
$=\text{Rs. }12000$
Therefore, simple interest $(I) = Rs. 12000$
Now, Amount $= P + I = Rs. 25000 + Rs. 12000 = Rs. 37000$
Hence, the correct option is $(b).$
View full question & answer→MCQ 111 Mark
If a sum of $Rs. 2000$ is lent out at $2\%$ per annum for $10$ years under simple interest, then the amount is:
- A
$Rs. 1400$
- ✓
$Rs. 2400$
- C
$Rs. 200$
- D
$Rs. 1500$
AnswerCorrect option: B. $Rs. 2400$
It is given that,
Sum $(P) = Rs. 2000$
Rate $(R) = 2\%$
Time $(T) = 10$ years
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{2000\ \times\ 2\ \times\ 10}{100}$
$=\text{Rs. }400$
Amount $= I + P = Rs. 400 + Rs. 2000 = Rs. 2400$
Hence, the correct option is $(b).$
View full question & answer→MCQ 121 Mark
At simple interest a sum becomes $\frac{49}{40}$ of itself in $2\frac{1}{2}$ years. The rate of interest per annum is:
AnswerAmount $=\frac{49}{40}$ times the sum $=\frac{49}{40}\text{P}$
Simple interest $(I) =$ Amount - Sum $=\frac{49}{40}\text{P}-\text{P}=\frac{9}{40}\text{P}$
Let the sum $(P)$ be $x.$
Then, simple interest $(I) =\frac{9}{40}\text{x}$
Rate $(R) = R\%$
Time $ (T) =2\frac{1}{2}\text{ years}=\frac{5}{2}\text{ years}$
$\text{I}=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$\Rightarrow\text{R}=\frac{100\ \times\ \text{I}}{\text{P }\times\text{ T}}$
$=\frac{100\ \times\frac{9}{40}\text{x}}{\text{x } \times\ \frac{5}{2}}$
$=\frac{45}{5}$
$=9\%$
Hence, the correct option is $(d).$
View full question & answer→MCQ 131 Mark
The simple interest for $Rs. 1500$ at $8\%$ per annum for $3$ years is:
- A
$Rs. 400$
- ✓
$Rs. 360$
- C
$Rs. 450$
- D
$Rs. 500$
AnswerCorrect option: B. $Rs. 360$
It is given that,
Sum $(P) = Rs. 1500$
Rate $(R) = 8\%$
Time $(T) = 3$ years
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{1500\ \times\ 8\ \times\ 3}{100}$
$=\text{Rs. }360$
Therefore, simple interest $(I) = Rs. 360$
Hence, the correct option is $(b).$
View full question & answer→MCQ 141 Mark
Which of the following yields maximum interest for $2$ years$?$
- A
$Rs. 1500$ at $8\%$ per annum
- B
$Rs. 1000$ at $11\%$ per annum
- C
$Rs. 2000$ at $5\%$ per annum
- ✓
$Rs. 900$ at $20\%$ per annum
AnswerCorrect option: D. $Rs. 900$ at $20\%$ per annum
$a.$ It is given that,
Sum $(P_1) = Rs. 1500$
Rate $(R_1) = 8\%$
Time $(T_1) = 2$ years
$\text{I}_1=\frac{\text{P}_1\ \times\ \text{R}_1\ \times\ \text{T}_1}{100}$
$\text{I}_1=\frac{1500\ \times\ 8\ \times\ 2}{100}$
$=240\ ...(\text{i})$
$b.$ It is given that,
Sum $(P_2) = Rs. 1000$
Rate $(R_2) = 11\%$
Time $(T_2) = 2$ years
$\text{I}_2=\frac{\text{P}_2\ \times\ \text{R}_2\ \times\ \text{T}_2}{100}$
$\text{I}_2=\frac{1000\ \times\ 11\ \times\ 2}{100}$
$=220\ ...(\text{ii})$
$c.$ It is given that,
Sum $(P_3) = Rs. 2000$
Rate $(R_3) = 5\%$
Time $(T_3) = 2$ years
$\text{I}_3=\frac{\text{P}_3\ \times\ \text{R}_3\ \times\ \text{T}_3}{100}$
$\text{I}_3=\frac{2000\ \times\ 5\ \times\ 2}{100}$
$=200\ ...(\text{iii})$
$d.$ It is given that,
Sum $(P_4) = Rs. 900$
Rate $(R_4) = 20\%$
Time $(T_4) = 2$ years
$\text{I}_4=\frac{\text{P}_4\ \times\ \text{R}_4\ \times\ \text{T}_4}{100}$
$\text{I}_4=\frac{900\ \times\ 20\ \times\ 2}{100}$
$=360\ ...(\text{iv})$
From $(i), (ii), (iii)$ and $(iv),$
$Rs. 900$ at $20\%$ per annum yields maximum interest for $2$ years.
Hence, the correct option is $(d)$.
View full question & answer→MCQ 151 Mark
If the simple interest on a certain sum for $2$ years at the rate of $5\%$ per annum is $Rs. 4000,$ then the sum is:
- A
$Rs. 46000$
- B
$Rs. 44000$
- ✓
$Rs. 40000$
- D
$Rs. 48000$
AnswerCorrect option: C. $Rs. 40000$
We know, simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
It is given that,
$T = 2$ years
$R = 5\%$
$I = Rs. 4000$
Then,
$4000=\frac{\text{P}\ \times\ 5\ \times\ 2}{100}$
$\Rightarrow4000=\frac{10\text{P}}{100}$
$\Rightarrow\text{P}=40000$
Thus, $P = Rs. 40000$
Hence, the correct option is $(c).$
View full question & answer→MCQ 161 Mark
At which rate per cent per annum simple interest will a sum treble itself in 16 years?
MCQ 171 Mark
The simple interest on a certain sum is $\frac{16}{25}$ of the sum. If the rate per cent per annum and the time are numerically equal, then the rate per cent is
View full question & answer→MCQ 181 Mark
The simple interest at $R \%$ per annum for $n$ years will be $₹ n$ on a sum of
- A
- B
- ✓
₹$\frac{100}{R}$
- D
₹$\frac{100}{n^2}$
AnswerCorrect option: C. ₹$\frac{100}{R}$
View full question & answer→MCQ 191 Mark
$a, b$ and $c$ are three sums of money such that $b$ is the simple interest on $a$ and $c$ is the simple interest on $b$ for the same time and same rate. Which is the following is correct?
- A
$a b c=1$
- B
$c^2=a b$
- ✓
$b^2=a c$
- D
$a^2=b c$
AnswerCorrect option: C. $b^2=a c$
View full question & answer→MCQ 201 Mark
In what time will a sum of ₹ 8000 amount to ₹ 8360 at $6 \%$ per annum simple interest?
- A
- ✓
- C
$1 \frac{1}{4}$ months
- D
$1 \frac{1}{2}$ years
View full question & answer→MCQ 211 Mark
At what rate per cent per annum simple interest will a sum double itself in 10 years?
- A
$8 \%$
- ✓
$10 \%$
- C
$12 \%$
- D
$12 \frac{1}{2} \%$
AnswerCorrect option: B. $10 \%$
View full question & answer→MCQ 221 Mark
At simple interest a sum becomes $\frac{49}{40}$ of itself in $2 \frac{1}{2}$ years. The rate of interest per annum is
- A
$7 \%$
- B
$8 \%$
- C
$12 \%$
- ✓
$9 \%$
AnswerCorrect option: D. $9 \%$
View full question & answer→MCQ 231 Mark
If interest on ₹ x for 2 years at $R \%$ per annum is ₹ 80 , then interest on ₹ 2 x for one year at $R \%$ per annum is
View full question & answer→MCQ 241 Mark
If a sum of ₹ 2000 is lent out at $2 \%$ per annum for 10 years under simple interest, then the amount is
View full question & answer→MCQ 251 Mark
If a sum of ₹ 3000 is lent out at $3 \%$ per annum for 20 years under simple interest, then the amount at the end of $20^{\text {th }}$ year is
View full question & answer→MCQ 261 Mark
Which of the following yields maximum interest for 2 years?
- A
₹ 1500 at $8 \%$ per annum
- B
₹ 1000 at $11 \%$ per annum
- C
₹ 2000 at $5 \%$ per annum
- ✓
₹ 900 at $20 \%$ per annum
AnswerCorrect option: D. ₹ 900 at $20 \%$ per annum
View full question & answer→MCQ 271 Mark
The difference between the interest obtained for ₹ 1000at $12 \%$ per annum for 3 years and that for ₹ 1500 at $8 \%$ per annum for $1 \frac{1}{2}$ years is
View full question & answer→MCQ 281 Mark
The simple interest for ₹ 1500 at $8 \%$ per annum for 3 years is
View full question & answer→MCQ 291 Mark
The amount on ₹ 25,000 at $8 \%$ per annum for 6 years under simple interest is
View full question & answer→MCQ 301 Mark
In how many years will a certain sum become 3 times itself at $25 \%$ per annum under simple interest?
View full question & answer→MCQ 311 Mark
If the simple interest on a certain sum for 2 years at the rate of $5 \%$ per annum is $₹ 4000$, then the sum is
View full question & answer→