MCQ - Maths STD 7 Questions - Vidyadip

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15 questions · auto-graded multiple-choice test.

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:

✓
$8\%$
B
$4\%$
C
$6\%$
D
$12\%$

Answer

Correct option: A.

$8\%$

Let 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 $(a).$

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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
$Rs. 200$

Answer

Correct 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
$\text{I}_1=\frac{\text{P}_1\ \times\ \text{R}_1\ \times\ \text{T}_1}{100}$
$=\frac{1000\ \times\ 12\ \times\ 3}{100}$
$=\text{Rs. }360\ ...(\text{i})$
$\operatorname{Sum}\left(P_2\right)= Rs. 1500$
Rate $\left(R_2\right)=8 \%$
Time $\left(T_2\right)=1 \frac{1}{2}$ year $=\frac{3}{2}$ year
$I_2=\frac{P_2 \times R_2 \times T_2}{100}$
$=\frac{1500 \times 8 \times 3}{100 \times 2}$
$=\text { Rs. } 180 \ldots \text { (ii) }$
Subtracting $(ii)$ from $(i),$ we get
$I_2-I_1=\text { Rs. } 360-\text { Rs. } 180$
$=\text { Rs. } 180$
Hence, the correct option is $(c).$

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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 $20^{th}$ year is:

A
$Rs. 1800$
B
$Rs. 1080$
C
$Rs. 3600$
✓
$Rs. 4800$

Answer

Correct option: D.

$Rs. 4800$

It is given that,
Sum $(P)= Rs. 3000$
Rate $(R)=3 \%$
Time $(T)=20$ years
$I =\frac{ P \times R \times T }{100}$
$=\frac{3000 \times 3 \times 20}{100}$
$= Rs. 1800$
Amount $=I+P= Rs. 1800+ Rs. 3000= Rs. 4800$
Hence, the correct option is $(c).$

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MCQ 41 Mark

At what rate percent per annum simple interest will a sum double itself in $10$ years?

A
$8\%$
✓
$10\%$
C
$12\%$
D
$12\frac{1}{2}\%$

Answer

Correct option: B.

$10\%$

Amount $= 2$ 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 $(b).$

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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

Answer

Correct option: C.

Rs. 80

It is given that,

$\text { Sum }\left(P_1\right)=\text { Rs. } x$

$\text { Rate }\left(R_1\right)=R \%$

$\text { Time }\left(T_1\right)=2 \text { years }$

$\text { Interest }\left(I_1\right)=\text { Rs. } 80$

$I_1=\frac{P_1 \times R_1 \times T_1}{100}$

$\Rightarrow 80=\frac{x \times R \times 2}{100}$

$\Rightarrow \frac{2 R x}{100}=80 \ldots \text { (i) }$

Now,

$\text { Sum }\left(P_2\right)=\text { Rs. } 2 x$

$\text { Rate }\left(R_2\right)=R \%$

$\text { Time }\left(T_2\right)=1 \text { year }$

$I_2=\frac{P_2 \times R_2 \times T_2}{100}$

$=\frac{2 x \times R \times 1}{100}$

$=\frac{2 Rx}{100}$

$=80[\text { From (i) }]$

Therefore, $I _2=$ Rs. 80

Hence, the correct option is (c).

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MCQ 61 Mark

The simple interest at $R\%$ per annum for $n$ years will be $Rs. n$ on a sum of:

A
$\text{Rs. }\text{n}$
B
$\text{Rs. }100\text{n}$
✓
$\text{Rs.}\frac{100}{\text{R}}$
D
$\text{Rs.}\frac{100}{\text{n}^2}$

Answer

Correct 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 $(c).$

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MCQ 71 Mark

At which rate percent per annum simple interest will a sum triple itself in $16$ years?

A
$12\%$
B
$10.5\%$
C
$11.5\%$
✓
$12.5\%$

Answer

Correct option: D.

$12.5\%$

Amount $= 3$ 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 $(d).$

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MCQ 81 Mark

In what time will a sum of $Rs. 8000$ amount to $Rs. 8360$ at $6\%$ per annum simple interest?

A
$8\text{ month}$
✓
$9\text{ month}$
C
$1\frac{1}{4}\text{ month}$
D
$1\frac{1}{2}\text{ year}$

Answer

Correct 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 $(b).$

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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
$c^2=a b$
✓
$b^2= ac$
D
$a^2=b c$

Answer

Correct option: C.

$b^2= ac$

It is given that,
Simple interest $\left(I_1\right)=b$
Sum $\left(P_1\right)=a$
Rate $\left(R_1\right)=R \%$
Time $\left(T_1\right)=T$ years
$I _1=\frac{ P _1 \times R _1 \times T _1}{100}$
$\Rightarrow b =\frac{ a \times R \times T }{100}$
$\Rightarrow R \times T =\frac{100 b}{ a } \ldots$
Also,
Simple interest $\left(I_2\right)= c$
Sum $\left(P_2\right)=b$
Rate $\left(R_2\right)=R \%$
Time $\left(T_2\right)=T$ years
Now,
$I_2=\frac{P_2 \times R_2 \times T_2}{100}$
$\Rightarrow c=\frac{b \times R \times T}{100}$
$\Rightarrow R \times T=\frac{100 c}{b} \ldots$
On equating $(i)$ and $(ii),$ we get
$\frac{100 b}{a}=\frac{100 c}{b}$
$\Rightarrow b^2=a c$
Hence, the correct option is $(d).$

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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
$Rs. 47000$

Answer

Correct 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 $(b).$

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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
$Rs. 1500$

Answer

Correct 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 $(b).$

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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:

A
$7\%$
B
$8\%$
C
$12\%$
✓
$9\%$

Answer

Correct option: D.

$9\%$

Amount $=\frac{49}{40}$ 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 $(d).$

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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
$Rs. 500$

Answer

Correct 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 $(b).$

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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

Answer

Correct option: D.

$Rs. 900$ at $20 \%$ per annum

It is given that,
$\text { Sum }\left(P_1\right)=R s . x$
$\text { Rate }\left(R_1\right)=R \%$
$\text { Time }\left(T_1\right)=2 \text { years }$
$\text { Interest }\left(I_1\right)=\text { Rs. } 80$
$I_1=\frac{P_1 \times R_1 \times T_1}{100}$
$\Rightarrow 80=\frac{x \times R \times 2}{100}$
$\Rightarrow \frac{2 Rx}{100}=80 \ldots \text { (i) }$
Now,
Sum $\left(P_2\right)=\text { Rs. } 2 x$
Rate $\left(R_2\right)=R \%$
Time $\left(T_2\right)=1$ year
$I_2=\frac{P_2 \times R_2 \times T_2}{100}$
$=\frac{2 x \times R \times 1}{100}$
$=\frac{2 Rx}{100}$
$=80[\text { From (i) }]$
Therefore, $I _2= Rs. 80$
Hence, the correct option is $(c).$

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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
$Rs. 48000$

Answer

Correct 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 $(c).$

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