RD Sharma solution class 7 chapter 13 Simple Interest Objective Type Questions

Objective Type Questions

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Question 1:

If the simple interest on a certain sum for 2 years at the rate of 5% per annum is ₹4000, then the sum is

(a) ₹46,000
(b) ₹44,000
(c) ₹40,000
(d) ₹48,000

Answer 1:

We know, $I=\frac{P\times T\times R}{100}$

It is given that,
T = 2 years
R = 5%
I = ₹4000

Then,
$$\begin{gathered} 4000=\frac{P\times 5\times 2}{100} \\ \Rightarrow 4000=\frac{10P}{100} \\ \Rightarrow P=40000 \end{gathered}$$

Thus, P = ₹40,000

Hence, the correct option is (c).

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Question 2:

In how many years will a certain sum become 3 times itself at 25% per annum under simple interest?

(a) 5
(b) 8
(c) 12
(d) 6

Answer 2:

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) = 25%
Time = T

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow T=\frac{100\times I}{P\times R} \\ =\frac{100\times 2x}{x\times 25} \\ =4\times 2 \\ =8 \mathrm{years} \end{gathered}$$

Hence, the correct option is (b).

Question 3:

The amount on ₹25,000 at 8% per annum for 6 years under simple interest is

(a) ₹35,000
(b) ₹37,000
(c) ₹45,000
(d) ₹47,000

Answer 3:

It is given that,
Sum (P) = ₹25,000
Rate (R) = 8%
Time (T) = 6 years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ =\frac{25000\times 8\times 6}{100} \\ =12000 \end{gathered}$$

Therefore, simple interest (I) = ₹12,000

Now, Amount = P + I = ₹25,000 + ₹12,000 = ₹37,000

Hence, the correct option is (b).

Question 4:

The simple interest for ₹1500 at 8% per annum for 3 years is

(a) ₹400
(b) ₹360
(c) ₹450
(d) ₹500

Answer 4:

It is given that,
Sum (P) = ₹1500
Rate (R) = 8%
Time (T) = 3 years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ =\frac{1500\times 8\times 3}{100} \\ =360 \end{gathered}$$

Therefore, simple interest (I) = ₹360

Hence, the correct option is (b).

Question 5:

The difference between the interest obtained for ₹1000 at 12% per annum for 3 years and that for ₹1500 at 8% per annum for $1\frac{1}{2}$ years is

(a) ₹360
(b) ₹300
(c) ₹180
(d) ₹200

Answer 5:

It is given that,
Sum (P₁) = ₹1000
Rate (R₁) = 12%
Time (T₁) = 3 years

$$\begin{gathered} I_1=\frac{P_1\times R_1\times T_1}{100} \\ =\frac{1000\times 12\times 3}{100} \\ =360 ....\left(1\right) \end{gathered}$$

Sum (P₂) = ₹1500
Rate (R₂) = 8%
Time (T₂) = $1\frac{1}{2}$ years = $\frac{3}{2}$ years

$$\begin{gathered} I_2=\frac{P_2\times R_2\times T_2}{100} \\ =\frac{1500\times 8\times 3}{100\times 2} \\ =180 ....\left(2\right) \end{gathered}$$

Subtracting (2) from (1), we get
$I_2-I_1=360-180=180$

Hence, the correct option is (c).

Question 6:

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
(d) ₹900 at 20% per annum

Answer 6:

(a) It is given that,
Sum (P₁) = ₹1500
Rate (R₁) = 8%
Time (T₁) = 2 years

$$\begin{gathered} I_1=\frac{P_1\times R_1\times T_1}{100} \\ =\frac{1500\times 8\times 2}{100} \\ =240 ....\left(1\right) \end{gathered}$$

(b) It is given that,
Sum (P₂) = ₹1000
Rate (R₂) = 11%
Time (T₂) = 2 years

$$\begin{gathered} I_2=\frac{P_2\times R_2\times T_2}{100} \\ =\frac{1000\times 11\times 2}{100} \\ =220 ....\left(2\right) \end{gathered}$$

(c) It is given that,
Sum (P₃) = ₹2000
Rate (R₃) = 5%
Time (T₃) = 2 years

$$\begin{gathered} I_3=\frac{P_3\times R_3\times T_3}{100} \\ =\frac{2000\times 5\times 2}{100} \\ =200 ....\left(3\right) \end{gathered}$$

(d) It is given that,
Sum (P₄) = ₹900
Rate (R₄) = 20%
Time (T₄) = 2 years

$$\begin{gathered} I_4=\frac{P_4\times R_4\times T_4}{100} \\ =\frac{900\times 20\times 2}{100} \\ =360 ....\left(4\right) \end{gathered}$$

From (1), (2), (3) and (4),
₹900 at 20% per annum yields maximum interest for 2 years.
​
Hence, the correct option is (d).

Question 7:

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^th year is

(a) ₹1800
(b) ₹1080
(c) ₹3600
(d) ₹4800

Answer 7:

It is given that,
Sum (P) = ₹3000
Rate (R) = 3%
Time (T) = 20 years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ =\frac{3000\times 3\times 20}{100} \\ =1800 \end{gathered}$$

Amount = I + P = ₹1800 + ₹3000 = ₹4800

Hence, the correct option is (d).

Question 8:

If a sum of ₹2000 is lent out at 2% per annum for 10 years under simple interest, then the amount is

(a) ₹1400
(b) ₹2400
(c) ₹200
(d) ₹1500

Answer 8:

It is given that,
Sum (P) = ₹2000
Rate (R) = 2%
Time (T) = 10 years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ =\frac{2000\times 2\times 10}{100} \\ =400 \end{gathered}$$

Amount = I + P = ₹400 + ₹2000 = ₹2400

Hence, the correct option is (b).

Question 9:

If interest on ₹x for 2 years at R% per annum is ₹80, the interest on ₹2x for one year at R% per annum is

(a) ₹160
(b) ₹40
(c) ₹80
(d) ₹120

Answer 9:

It is given that,
Sum (P₁) = ₹x
Rate (R₁) = R%
Time (T₁) = 2 years
Interest (I₁) = ₹80

$$\begin{gathered} I_1=\frac{P_1\times R_1\times T_1}{100} \\ \Rightarrow 80=\frac{x\times R\times 2}{100} \\ =\frac{2Rx}{100} ...\left(1\right) \end{gathered}$$

Now,
Sum (P₂) = ₹2x
Rate (R₂) = R%
Time (T₂) = 1 year

$$\begin{gathered} I_2=\frac{P_2\times R_2\times T_2}{100} \\ =\frac{2x\times R\times 1}{100} \\ =\frac{2Rx}{100} \\ =80 \left[\mathrm{From} \left(1\right)\right] \end{gathered}$$

Therefore, I₂ = ₹80

Hence, the correct option is (c).

Question 10:

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%
(d) 9%

Answer 10:

Amount = $\frac{49}{40}$ times the sum = $\frac{49}{40}$P

Simple interest (I) = Amount − Sum = $\frac{49}{40}$P − P = $\frac{9}{40}$P

Let the sum (P) be x.
Then, simple interest (I) = $\frac{9}{40}$x
Rate (R) = R%
Time (T) = $2\frac{1}{2}$ years = $\frac{5}{2}$ years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow R=\frac{100\times I}{P\times T} \\ =\frac{100\times {\displaystyle \frac{9}{40}}x}{x\times {\displaystyle \frac{5}{2}}} \\ =\frac{45}{5} \\ =9\% \end{gathered}$$

Hence, the correct option is (d).

Question 11:

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

(a) 8%
(b) 10%
(c) 12%
(d) $12\frac{1}{2}$%

Answer 11:

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

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow R=\frac{100\times I}{P\times T} \\ =\frac{100\times x}{x\times {\displaystyle 10}} \\ =10\% \end{gathered}$$

Hence, the correct option is (b).

Question 12:

In what time will a sum of ₹8000 amount to ₹8360 at 6% per annum simple interest?

(a) 8 months
(b) 9 months
(c) $1\frac{1}{4}$ months
(d) $1\frac{1}{2}$ years

Answer 12:

It is given that,
Amount = ₹8360
Sum = ₹8000

Simple interest (I) = Amount − Sum = ₹8360 − ₹8000 = ₹360

Also,
Rate (R) = 6%
Time (T) = T years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow T=\frac{100\times I}{P\times R} \\ =\frac{100\times 360}{8000\times 6} \\ =\frac{3}{4} \mathrm{years} \\ =\frac{3}{4}\times 12 \mathrm{months} \\ =9 \mathrm{months} \end{gathered}$$

Hence, the correct option is (b).

Question 13:

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) abc = 1
(b) c² = ab
(c) b² = ac
(d) a² = bc

Answer 13:

It is given that,
Simple interest (I₁) = b
Sum (P₁) = a
Rate (R₁) = R%
Time (T₁) = T years

Now,
$$\begin{gathered} I_1=\frac{P_1\times R_1\times T_1}{100} \\ \Rightarrow b=\frac{a\times R\times T}{100} \\ \Rightarrow R\times T=\frac{100b}{a} ....\left(1\right) \end{gathered}$$

Also,
Simple interest (I₂) = c
Sum (P₂) = b
Rate (R₂) = R%
Time (T₂) = T years

Now,
$$\begin{gathered} I_2=\frac{P_2\times R_2\times T_2}{100} \\ \Rightarrow c=\frac{b\times R\times T}{100} \\ \Rightarrow R\times T=\frac{100c}{b} ....\left(2\right) \end{gathered}$$

On equating (1) and (2), we get
$$\begin{gathered} \frac{100b}{a}=\frac{100c}{b} \\ \Rightarrow b^2=ac \end{gathered}$$

Hence, the correct option is (c).

Question 14:

The simple interest at R% per annum for n years will be ₹n on a sum of

(a) ₹n
(b) ₹100n
(c) ₹$\frac{100}{n}$
(d) ₹$\frac{100}{n^2}$

Answer 14:

It is given that,
Simple interest (I) = ₹n
Rate (R) = R%
Time (T) = n years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow P=\frac{100\times I}{R\times T} \\ =\frac{100\times n}{R\times n} \\ =\frac{100}{R} \end{gathered}$$

Hence, the correct option is (c).

Question 15:

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

(a) 8%
(b) 4%
(c) 6%
(d) 12%

Answer 15:

Let the sum (P) be ₹x
Then, the simple interest (I) = ₹$\frac{16}{25}$x

Also,
Rate (R) = R%
Time (T) = R years    (∵ the rate percent per annum and the time are numerically equal)

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow R=\frac{100\times I}{P\times T} \\ \Rightarrow R=\frac{100\times {\displaystyle \frac{16}{25}}x}{x\times R} \\ \Rightarrow R\times R=\frac{64x}{x} \\ \Rightarrow R\times R=8\times 8 \\ \Rightarrow R=8\% \end{gathered}$$

Hence, the correct option is (a).

Question 16:

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

(a) 12%
(b) 10.5%
(c) 11.5%
(d) 12.5%

Answer 16:

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

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow R=\frac{100\times I}{P\times T} \\ =\frac{100\times 2x}{x\times {\displaystyle 16}} \\ =12.5\% \end{gathered}$$

Hence, the correct option is (d).