Simple Interest Questions and Answers

Q1 :

What principal will amount of Rs. 560 in 3 years at 4 p.c. per annum simple interest?

A

425

B

450

C

475

D

500

Check Answer

Right Answer: D

500

Description:

$text{Principal } = frac{560 times 100}{100 + 4 times 3} = text{Rs.} 500$

Q2 :

At what rate of simple interest per annum will a sum of money become three times its original amount in 25 years?

A

5%

B

4%

C

6%

D

8%

Check Answer

Right Answer: D

8%

Description:

Rs. 100 becomes Rs. 300 means interest is Rs. 200 on Rs. 100 in 25 years

$text{Rate} = frac{200 times 100}{100 times 25} = 8%$

Q3 :

The simple interest earned on a certain amount is one-ninth of the principal, and the number of years is the same as the annual rate of interest. Determine the rate of interest per annum.

A

$10{%}$

B

${frac {1}{3}% }$

C

$3%$

D

$3 {frac{1}{3}%}$

Check Answer

Right Answer: D

$3 {frac{1}{3}%}$

Description:

$=frac{1}{9} text{P} = frac{text{P} times text{R} times text{T} }{100}, text{but } r = t$

Q4 :

A man buys land and gives for it twenty five times the annual rent. What percent rate of interest does he get for his money?

A

1%

B

2%

C

3%

D

4%

Check Answer

Right Answer: D

4%

Description:

Let the annual rent be $x$ so that the investment in $25x$ .

$text{ Rate } = frac{x times 100 }{25 times x} = 4%$

Q5 :

If the compound interest on a sum for 3 years at 5% is Rs. 1324.05, what is the simple interest ?

A

Rs. 1060

B

Rs. 1160

C

Rs. 1260

D

Rs. 1360

Check Answer

Right Answer: C

Rs. 1260

Description:

$text{ A = P } times Big(1 + frac{r}{100} Big)^n$

$= text{P } times Big(1 + frac{5}{100}Big)^3 = text{P } times Big(frac{9361}{8000}Big)$

$therefore$ If P = Rs. 8000, A = Rs. 9261

$therefore$ C.I. = Rs. 1261

Simple interest on Rs. 8000 for 3 years at 5% = Rs. 1200

Now if C.I. = Rs. 1261, SI = Rs. 1200 and if C.I. = Rs. 1324.50 then

$text{S.I. } = frac{1200}{1261} times 1324.05 = text{ Rs. } 1260$

Q6 :

An amount invested at 5% simple interest annually becomes Rs. 504 after 4 years. If the same principal is invested at 10% simple interest per annum for 2.5 years, what will be the total amount?

A

Rs. 420

B

Rs. 450

C

Rs. 525

D

Rs. 550

Check Answer

Right Answer: C

Rs. 525

Description:

Let the principal amount P.

$therefore text{ P } + frac{text{ P } times 5 times 4}{100} = 504$
$Rightarrow 120 text{ P } = 50400 Rightarrow text{ P } = 420$
$therefore text{ The amount of Rs. } 420 text{ at }$
$10% text{ p.a., for } 2 frac{1}{2} text{ years }$
$= 420 + frac{420 times 10 times 5}{100 times 2}$
=Rs. 525

Q7 :

A certain sum amounts to Rs. 1586 in 2 yr and Rs. 1729 in 3 yr. Find the rate and the sum.

A

8%, Rs. 1200

B

9%, Rs. 1300

C

10%, Rs. 1000

D

11%, Rs. 1300

Check Answer

Right Answer: D

11%, Rs. 1300

Description:

Here, A₁ = Rs. 1586, t₁ = 2 yr, A₂ = 1729 and t₂ = 3 yr

Therefore, Required principle $= dfrac{A_2t_1 - A_1t_2}{t_1 - t_2} = dfrac{1729 times 2 - 1586 times 3}{2-3}$

= Rs. 1300

and required rate R $= bigg[dfrac{(A_2 - A_1) times 100}{A_1t_2 - A_2t_1} bigg] %$

$= dfrac{(1729 - 1586) times 100}{1586times 3 - 1729times 2} = dfrac{143 times 100}{1300} = 11%$

Q8 :

The simple interest on a sum of money at 10% per annum for 6 yr is half the sum. Then, the sum is

A

Rs. 5000

B

not possible

C

Rs. 4000

D

Rs. 6000

Check Answer

Right Answer: B

not possible

Description:

Let the sum (principal) be Rs. $x$ .
Therefore, Simple interest = Rs. $dfrac{x}{2}$

and T = 6 yr, R = 10% per annum

$therefore text{SI } = dfrac{P times R times T}{100}$

$Rightarrow dfrac{x}{2} = dfrac{x times 10 times 6}{100} Rightarrow dfrac{1}{2} = dfrac{6}{10}$

Which is not true, so it is not a possible case.

Q9 :

A certain amount invested at simple interest becomes Rs. 1040 after 3 years and increases to Rs. 1360 after 7 years. Determine the initial principal.

A

Rs. 750

B

Rs. 800

C

Rs. 900

D

Rs. 1000

Check Answer

Right Answer: B

Rs. 800

Description:

Simple interest for 4 yr
= Rs. (1360 − 1040) = Rs. 320

Simple interest for 3 yr

= Rs. $bigg(dfrac{320}{4} times3 bigg)$ = Rs. 240

$therefore$ Sum or principle = Rs. (1040 − 240)
= Rs. 800

Q10 :

Vijay buys a house by paying Rs. 8000 in cash and Rs. 9600 on a 5-year credit at 4% per annum simple interest. What is the house's cash price?

A

Rs. 10000

B

Rs. 9600

C

Rs. 17000

D

Rs. 16000

Check Answer

Right Answer: D

Rs. 16000

Description:

Let the amount remaining to pay be Rs. $x$ .
$therefore$ Price of house = Rs. $(x + 8000)$

$begin{aligned} & Rightarrow 9600 - dfrac{x times 4 times 5}{100} =x ~ & Rightarrow 9600 - dfrac{x}{5} =x ~ & Rightarrow 9600 =dfrac{6x}{5} Rightarrow dfrac{9600 times 5}{6} = x ~ & Rightarrow x = 8000 end{aligned}$

$therefore$ Cash price of the house = Rs. (8000 + 8000) = Rs. 16000

Q11 :

A sum was invested at simple interest for 2 years at a certain rate. If the rate had been 3% higher, the interest would have been Rs. 72 more. What is the principal amount?

A

1200

B

1600

C

1900

D

1400

Check Answer

Right Answer: A

1200

Description:

Let the sum be Rs. $x$ and the original rate $r%$ , then
Simple interest $= dfrac{x times r times 2}{100}$

Now, rate is increased by 3%.

Therefore, New rate $= ( r + 3)%$

Because, Simple interest $= dfrac{x times (r+3) times 2}{100}$

$begin{aligned} &therefore dfrac{x times (r + 3) times 2}{100} - dfrac{x times r times 2}{100} = 72 \ &Rightarrow dfrac{(xr + 3x)2}{100} - dfrac{2xr}{100} = 72 \ &Rightarrow dfrac{2xr + 6x -2xr}{100} = 72 \ &therefore x = 1200 end{aligned}$

Q12 :

The simple interest on Rs. 1230 for 2 years is Rs. 10 more than the simple interest on Rs. 1130 for the same period. What is the rate of interest?

A

5%

B

6%

C

8%

D

2%

Check Answer

Right Answer: A

5%

Description:

Here, $I_1 - I_2$ = Rs. 10, $P_1$ = Rs. 1230,
$P_2$ = Rs. 1130 and T = 2 yr

According to formula,

$begin{aligned} &I_2 - I_1 = dfrac{T times R times (P_2 - P1)}{100} \ &-10 = dfrac{R times 2 (1130 - 1230)}{100} \ &-10 = dfrac{-200R}{100} \ &therefore R = 5% end{aligned}$