MCQ 11 Mark
Mark $(\checkmark)$ against the correct answer in the following: A borrows $Rs. 8000$ at $12\%$ per annum simple interest and $B$ borrows $Rs. 9100$ at $10\%$ per annum simple interest. In how many years will their amounts be equal$?$
- A
$18$ years
- B
$20$ years
- ✓
$22$ years
- D
$24$ years
AnswerCorrect option: C. $22$ years
$\mathrm{R}_1=12 \%$
$\mathrm{R}_2=10 \%$
$\mathrm{P}_1=\text { Rs. } 8000$
$\mathrm{P}_2=\text { Rs. } 9100$
Let their amounts be equal in $T$ years.
$\text { Amount }_1=\text { S.I }_1+\mathrm{P}_1$
$=\frac{\mathrm{P}_1 \times \mathrm{I}_1 \times \mathrm{T}}{100}+\mathrm{P}_1$
$=960 \mathrm{~T}+8000$
$\text { Amount }{ }_2=\text { S.I }_2+\mathrm{P}_2$
$=\frac{\mathrm{P}_2 \times \mathrm{r}_2 \times \mathrm{T}}{100}+\mathrm{P}_2$
$=\frac{9100 \times 10 \times \mathrm{T}}{100}+9100$
$=910 \mathrm{~T}+9100$
$\text { Amount }_1=\text { Amount }_2$
$\Rightarrow 960 \mathrm{~T}+8000=910 \mathrm{~T}+9100$
$\Rightarrow 960 \mathrm{~T}-910 \mathrm{~T}=9100-8000$
$\Rightarrow 50 \mathrm{~T}=1100$
$\Rightarrow \mathrm{~T}=22$
Hence, after $22$ years their amounts will be equal.
View full question & answer→MCQ 21 Mark
Mark $(\checkmark)$ against the correct answer in the following: A sum amounts to $Rs.3605$ in $219$ days at $5\%$ per annum. The sum is:
- A
$Rs. 3250$
- ✓
$Rs. 3500$
- C
$Rs. 3400$
- D
$Rs. 3550$
AnswerCorrect option: B. $Rs. 3500$
Amount $= Rs. 3605$
Time $=\frac{219}{365}$ days $=\frac{219}{365}$ days
Rate $= 5\%$ per annum
Amount $=\text{Sum}+\frac{\text{Sum}\times\text{Rate}\times\text{Time}}{100}$
Amount $=\text{Sum}\Big(1+\frac{\text{Rate}\times\text{Time}}{100}\Big)$
$\text{Sum}=\frac{3605}{1+\frac{5}{100}\times\frac{219}{365}}$
$=\frac{3605\times36500}{37595}$
$\text{Sum}=\text{Rs. }3500$
View full question & answer→MCQ 31 Mark
Mark $(\checkmark)$ against the correct answer in the following: In what time will $Rs. 6000$ amount to $Rs. 6360$ at $8\%$ interest per annum simple interest$?$
- ✓
$9\text{ months}$
- B
$\text{8 months}$
- C
$1\frac14\text{ years}$
- D
$1\frac12\text{ years}$
AnswerCorrect option: A. $9\text{ months}$
$P = Rs. 6000$
$A = Rs. 6360$
$S.I. = A - P = 6300 - 6000$
$= Rs. 360$
$\text{T}=\frac{\text{S.I.}\times100}{\text{P}\times\text{T}}=\frac{360\times100}{6000\times8}$
$=\frac68\text{ years}$
$=\frac67\times12\text{ months}$
$=\frac{72}{8}$
$=9\text{ months}$
View full question & answer→MCQ 41 Mark
Mark $(\checkmark)$ against the correct answer in the following: The simple interest on $Rs. 6250$ at $4\%$ per annum for $6$ months is:
- ✓
$Rs. 125$
- B
$Rs. 150$
- C
$Rs. 175$
- D
$Rs. 135$
AnswerCorrect option: A. $Rs. 125$
$Rs. 125$
Princepal $= Rs. 6250$
Simple interest $= 4\%$ per annum
Time $= 6$ months $=\frac12$ years
Simple interest $=\frac{\text{P}\times\text{r}\times\text{t}}{100}$
Simple interest $=\frac{6250\times4\times1}{100\times2}$
Simple interest $=\frac{250}{2}=\text{Rs. }125$
View full question & answer→MCQ 51 Mark
Mark $(\checkmark)$ against the correct answer in the following: The simple interest on a sum for $5$ years is $\frac25$ of the sum. The rate percent per annum is:
- A
$10\%$
- ✓
$8\%$
- C
$6\%$
- D
$12\frac12\%$
Answer
Times $= 5$ years
Simple interest $=\frac25\text{P}$
$\Rightarrow\frac{\text{P}\times\text{Rate}\times\text{time}}{100}=\frac{2}{5}\text{P}$
$\Rightarrow\frac{\text{Rate}\times5}{100}=\frac25$
$\Rightarrow\text{Rate}=\frac{2\times100}{5\times5}$
$\Rightarrow\text{Rate}=8\%$
View full question & answer→MCQ 61 Mark
Mark $(\checkmark)$ against the correct answer in the following: A sum of $Rs. 600$ amounts to $Rs. 720$ in $4$ years. What will it amount to if the rate of interest is increased by $2\%?$
- A
$Rs. 724$
- B
$Rs. 648$
- ✓
$Rs. 768$
- D
$Rs. 792$
AnswerCorrect option: C. $Rs. 768$
Let the rate be $R \%$
$S.I. = A - P$
$= 720 - 600$
$= Rs. 120$
Time $= 4$ years
$\text{R}=\frac{10\times\text{S.I.}}{\text{P}\times\text{T}}$
$\text{R}=\frac{100\times120}{600\times4}$
$=5$
Rate of interest $= 5\%$
Now,
$\text{R}=(5+2)\%=7\%$
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{600\times7\times4}{100}$
$\text{Rs. }168$
Amount $= S.I. + P$
$= 600 + 168$
$= Rs. 768$
View full question & answer→MCQ 71 Mark
Mark $(\checkmark)$ against the correct answer in the following: The simple interest at $x \%$ per annum for $x$ years will be $Rs. x$ on a sum of:
AnswerCorrect option: C. $\text{Rs. }\Big(\frac{100}{\text{x}}\Big)$
Simple interest $= Rs. x$
Rate $= x\%$ per annum
Time $= x$ years
Simple interest $=\frac{\text{Princepal}\times\text{Rate}\times\text{Time}}{100}$
$\Rightarrow\text{x}=\frac{\text{Princepal}\times\text{x}\times\text{x}}{100}$
$\Rightarrow\text{Principal}=\text{Rs. }\frac{100}{\text{x}}$
View full question & answer→MCQ 81 Mark
Mark $(\checkmark)$ against the correct answer in the following:
At simple interest a sum becomes $\frac65$ of itself in $2\frac12$ years. The rate of interest per annum is:
- A
$6\%$
- B
$7\frac12\%$
- ✓
$8\%$
- D
$9\%$
AnswerLet the sum be $Rs. x$
Rate of interest $= r\%$
Time $=2\frac12$ years $=\frac52$ years
Amount $=\frac65\times\text{Sum}$
Rate $= ?$
Amount $=\frac65\times\text{Sum}$
Principal $+\ S.I. =$ Amount
$\text{Principal}+\frac{\text{Principal}\times\text{Rate}\times\text{Time}}{100}=\frac65\times\text{Principal}$
$\Rightarrow\text{x}+\frac{\text{x}\times\text{r}\times5}{100\times2}=\frac65\text{x}$
$\Rightarrow\text{x}\Big(1+\frac{5\text{r}}{100\times2}\Big)=\frac65\text{x}$
$\Rightarrow1+\frac{\text{r}}{40}=\frac65$
$\Rightarrow\text{r}=40\times\frac15$
$\Rightarrow\text{r}=8$
So, the rate of interest is $8\%$
View full question & answer→MCQ 91 Mark
Mark $(\checkmark)$ against the correct answer in the following:A sum amounts to $Rs. 3626$ in $219$ days at $6\%$ per annum simple interest. The sum is:
- A
$Rs. 3000$
- B
$Rs. 3200$
- ✓
$Rs. 3500$
- D
$Rs. 3600$
AnswerCorrect option: C. $Rs. 3500$
$A = Rs. 3626$
$R = 6\%$
$T = 219$ days $=\frac{219}{365}\text{ years}$
Let the required sum be $Rs. x$
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{\text{x}\times6\times219}{100\times365}$
$=\frac{1314\text{x}}{36500}$
$\text{A}=\text{P}+\text{S.I.}$
$=\text{x}+\frac{1314\text{x}}{36500}$
$=\frac{36500\text{x}+1314\text{x}}{36500}$
$=\frac{1314\text{x}}{36500}$
But the amount is $Rs. 3626$
$\therefore\frac{37814\text{x}}{36500}=3626$
$\text{x}=\frac{3626\times36500}{37814}=3500$
The required sum is $Rs. 3500$
View full question & answer→MCQ 101 Mark
Mark $(\checkmark)$ against the correct answer in the following:
At which sum the simple interest at the rate of $3\frac34\%$ per annum will be $Rs. 210$ in $2\frac13$ years$?$
- A
$Rs. 1580$
- ✓
$Rs. 2400$
- C
$Rs. 2800$
- D
AnswerCorrect option: B. $Rs. 2400$
Rate $=3\frac34\%$ per annum
$=\frac{15}{4}\%$ per annum
Time $=2\frac13$ years
$=\frac73$ years
$\text{S.I.}=\frac{\text{P}\times\frac{15}{4}\times\frac{7}{3}}{100}$
$\Rightarrow\text{P}=\frac{210\times100}{\Big(\frac{15}{4}\times\frac{7}{3}\Big)}$
$\Rightarrow\text{P}=600\times4$
$\Rightarrow\text{P}=\text{Rs. }2400$
View full question & answer→MCQ 111 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The simple interest on a sum for $5$ years is $\frac{3}{3}$ of the sum. The rate percent per annum is:
- A
$8\%$
- B
$10\%$
- ✓
$12\%$
- D
$12\frac12\%$
AnswerCorrect option: C. $12\%$
Let the sum be $Rs. x$
Let the rate be $R \%$ per annum
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{\text{x}\times\text{R}\times5}{100}$
$=\frac{\text{Rx}}{20}$
$\therefore\frac{3\text{x}}{5}=\frac{\text{Rx}}{20}$
$\Rightarrow\text{R}=\frac{3\text{x}\times20}{5\text{x}}=12\%$
View full question & answer→MCQ 121 Mark
Mark $(\checkmark)$ against the correct answer in the following: In what time will $Rs. 8000$ amount to $Rs. 8360$ at $6\%$ per annum simple interest$?$
- A
$8\text{ months}$
- ✓
$9\text{ months}$
- C
$1\frac14\text{ years}$
- D
$1\frac12\text{ years}$
AnswerCorrect option: B. $9\text{ months}$
Let the time be $t$ years.
Principal $= Rs. 8000$
Amount $= Rs. 8360$
Rate $= 6\%$ per annum
Amount $=\text{Princepal}\Big(1+\frac{\text{Rate}\times\text{Times}}{100}\Big)$
$\frac{8360}{8000}=1+\frac{6\times\text{t}}{100}$
$\Rightarrow\frac{8360}{8000}-1=\frac{\text{6t}}{100}$
$\Rightarrow\text{t}=\Big(\frac{8360-8000}{8000}\Big)\times\frac{100}{6}$
$=\frac{360}{8000}\times\frac{100}{6}$
$=\frac68\times12\text{ months}$
$=9\text{ months}$
View full question & answer→MCQ 131 Mark
Mark $(\checkmark)$ against the correct answer in the following: $x, y$ and $z$ are three sums of money such that $y$ is the simple interest on $x$ and $z$ is the simple interest on $y$ for the same time and same rate. Which of the following is correct$?$
- A
$x y z=1$
- B
$z^2=x y$
- C
$x^2=y z$
- ✓
$y^2=z x$
AnswerCorrect option: D. $y^2=z x$
$\text{y}=\text{S.I.}\text{ on x}=\frac{\text{x}\times\text{R}\times\text{T}}{100}\ ...\text{(i)}$
$\text{z}=\text{S.I. on y}=\frac{\text{y}\times\text{R}\times\text{T}}{100}\ ...\text{(ii)}$
Dividing equation $(i)$ by $(ii):$
$\Rightarrow\frac{\text{y}}{\text{z}}=\Big(\frac{\text{x}\times\text{R}\times\text{T}}{100}\times\frac{100}{\text{y}\times\text{R}\times\text{T}}\Big)$
$\Rightarrow\frac{\text{y}}{\text{z}}=\frac{\text{x}}{\text{y}}$
$\Rightarrow\text{y}^2=\text{zx}$
View full question & answer→MCQ 141 Mark
Mark $(\checkmark)$ against the correct answer in the following: The simple interest at $x\%$ per annum for $x$ years will be $Rs. x$ on a sum of:
AnswerCorrect option: D. $\text{Rs.}\Big(\frac{100}{\text{x}}\Big)$
Let the sum be $Rs. P$
Times $= x$ years
Rate of interest
$r = x\%$ per annum
$S.I. = Rs. x$
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$\Rightarrow\text{P}=\frac{\text{x}\times\text{100}}{\text{x}\times\text{x}}$
$\text{P}=\text{Rs. }\frac{100}{\text{x}}$
View full question & answer→MCQ 151 Mark
Mark $(\checkmark)$ against the correct answer in the following:
At simple interest a sum becomes $\frac{49}{40}$ of it self in $\frac12$ years. The rate of interest per annum is:
- A
$7\%$
- B
$8\%$
- ✓
$9\%$
- D
$12\%$
AnswerLet the sum be $Rs.x$
$\text{A}=\frac{49\text{x}}{40}$
We know:
$A = P + S.I.$
$S.I. = A - P$
$=\Big(\frac{\text{49x}}{40}-\text{x}\Big)$
$=\frac{49\text{x}-40\text{x}}{40}$
$=\frac{9\text{x}}{40}$
Let the rate be $R\%$ per annum.
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$\Rightarrow\frac{9\text{x}}{40}=\frac{\text{x}\times\text{R}\times5}{100\times2}$
$\Rightarrow\text{R}=\frac{9\times20\times2}{10}$
$\Rightarrow\text{R}=9$
View full question & answer→MCQ 161 Mark
Mark $(\checkmark)$ against the correct answer in the following:In how much time would the simple interest on a certain sum be $0.125$ times the principal at $10\%$ per annum$?$
- ✓
$1\frac14\text{ years}$
- B
$1\frac34\text{ years}$
- C
$2\frac14\text{ years}$
- D
$2\frac34\text{ years}$
AnswerCorrect option: A. $1\frac14\text{ years}$
Rate $= 10\%$ per annum
Simple interest $= 0.125\ \times $ Principal
$\Rightarrow\frac{\text{Princepal}\times\text{Rate}\times\text{Time}}{100}=0.125\times\text{Principal}$
$\Rightarrow\frac{\text{Time}}{10}=0.125$
$\Rightarrow\text{Time}=1.25=1\frac14\text{ years}$
View full question & answer→MCQ 171 Mark
Mark $(\checkmark)$ against the correct answer in the following:
At what rate percent per annum simple interest will a sum double it self in $10$ years$?$
- A
$8\%$
- ✓
$10\%$
- C
$12\%$
- D
$12\frac12\%$
AnswerCorrect option: B. $10\%$
Let the sum be $Rs. x$ and the rate be $r\%$
Amount $= 2x$
$\Rightarrow\text{P}+\text{S.I.}=2\text{x}$
$\Rightarrow\text{P}+\frac{\text{P}\times\text{r}\times\text{t}}{100}=\text{2x}$
$\Rightarrow\text{x}\Big(1+\frac{\text{r}\times100}{100}\Big)=\text{2x}$
$\Rightarrow\frac{100+10\text{r}}{100}=2$
$\Rightarrow10\text{r}=200-100$
$\Rightarrow10\text{r}=100$
$\Rightarrow\text{r}=\frac{100}{10}$
$\Rightarrow\text{r}=10$
View full question & answer→MCQ 181 Mark
Mark $(\checkmark)$ against the correct answer in the following: At what rate percent per annum simple interest will a sum double it self in $10$ years$?$
- A
$8\%$
- ✓
$10\%$
- C
$12\%$
- D
$12\frac12\%$
AnswerCorrect option: B. $10\%$
Let the sum be $Rs. x$
Amount $Rs. 2x$
Time $= 10$ years
$S.I. = A - P = 2x - x = Rs. x$
$\therefore\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$\Rightarrow\text{x}=\frac{\text{x}\times\text{R}\times10}{100}$
$\Rightarrow\text{R}=\frac{\text{x}\times100}{\text{x}\times100}$
$\Rightarrow\text{R}=10\%$
View full question & answer→MCQ 191 Mark
At which sum will the simple interest at the rate of $3 \frac{3}{4} \%$ per annum be $₹ 210$ in $2 \frac{1}{3}$ years?
View full question & answer→MCQ 201 Mark
In how much time would the simple interest on a certain sum be 0.125 times the principal at $10 \%$ per annum?
- ✓
$1 \frac{1}{4}$ years
- B
$1 \frac{3}{4}$ years
- C
$2 \frac{1}{4}$ years
- D
$2 \frac{3}{4}$ years
AnswerCorrect option: A. $1 \frac{1}{4}$ years
View full question & answer→MCQ 211 Mark
x, y and z are three sums of money such that y is the simple interest on x and z is the simple
interest on y for the same time and same rate. Which of the following is correct?
- A
- B
$z^2=x y$
- C
$x^2=y z$
- ✓
$y^2=z x$
AnswerCorrect option: D. $y^2=z x$
View full question & answer→MCQ 221 Mark
A sum of ₹600 amounts to ₹ 720 in 4 years. What will it amount to if the rate of interest is increased by 2%?
MCQ 231 Mark
A borrows ₹ 8000 at $12 \%$ per annum simple interest and B borrows ₹ 9100 at $10 \%$ per annum simple interest. In how many years will their amounts be equal?
View full question & answer→MCQ 241 Mark
The simple interest on a sum for 5 years is $\frac{2}{5}$ of the sum. The rate per cent per annum is
View full question & answer→MCQ 251 Mark
The simple interest at $x \%$ per annum for $x$ years will be $₹ x$ on a sum of
AnswerCorrect option: C. $₹\left(\frac{100}{x}\right)$
View full question & answer→MCQ 261 Mark
At what rate per cent per annum simple interest will a sum double itself in 10 years?
MCQ 271 Mark
In what Ume will ₹8000 amount to₹ 8360 at 6% per annum simple interest?
- A
- ✓
- C
$1 \frac{1}{4}$ years
- D
$1 \frac{1}{2}$ years
View full question & answer→MCQ 281 Mark
At simple interest a sum becomes $\frac{6}{5}$ of itself in $2 \frac{1}{2}$ years. The rate of inerest per annum is
View full question & answer→MCQ 291 Mark
A sum amounts to ₹3605 In 219 days at 5% per annum. The sum is
MCQ 301 Mark
The simple interest on ₹ 6250 at 4% per annum for 6 months is