Simple Interest Questions and Answers

Q: Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.

\[ \text{SI} = \frac{P \times R \times T}{100} \]The rate \( 15\tfrac{2}{5}\% \) is 15.4%, and nine months is \( \tfrac{3}{4} \) of a year.\[ \text{SI} = \frac{78000 \times 15.4 \times 0.75}{100} \]\[ = 780 \times 15.4 \times 0.75 = 780 \times 11.55 = \text{Rs. } 9009 \]Leaving the period as 9 rather than \( \tfrac{9}{12} \) would inflate the answer twelvefold.

Q: Simple interest at x% for x years will come out to be Rs x on a sum of Rs?

\[ \text{SI} = \frac{P \times R \times T}{100} \]Both the rate and the time are \( x \), and the interest is also \( x \).\[ x = \frac{P \times x \times x}{100} = \frac{P x^{2}}{100} \]Dividing both sides by \( x \):\[ 1 = \frac{Px}{100} \quad\Longrightarrow\quad P = \frac{100}{x} \]Only one power of \( x \) survives the cancellation, which is what separates \( \tfrac{100}{x} \) from \( \tfrac{100}{x^{2}} \).

Q: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?

\[ \text{SI} = \frac{P \times R \times T}{100} \]The period \( 2\tfrac{2}{5} \) years is 2.4 years, and Rs. 1120 is the amount.\[ 1120 = P\left(1 + \frac{5 \times 2.4}{100}\right) = P(1.12) \]\[ P = \text{Rs. } 1000 \]The interest is Rs. 120, which is 12% of the principal - 5% a year for 2.4 years.

Q: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ 70 = \frac{P \times 3.5 \times 4}{100} = 0.14P \]\[ P = \frac{70}{0.14} = \text{Rs. } 500 \]Over four years at 3.5% the interest comes to 14% of the sum.

Q: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ \text{SI} = 900 - 750 = \text{Rs. } 150 \]\[ 150 = \frac{750 \times R \times 5}{100} = 37.5R \]\[ R = 4\% \]The Rs. 900 is the amount, so the principal must be subtracted first.

Q: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ 160 = \frac{800 \times R \times 4}{100} = 32R \]\[ R = 5\% \]The Rs. 160 is 20% of the principal, spread over four years - 5% a year.

Q: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?

\[ \text{SI} = \frac{P \times R \times T}{100} \]Under simple interest the yearly addition is constant, so the gap between the two amounts covers two years.\[ 1875 - 1725 = 150 \text{ over 2 years} \quad\Longrightarrow\quad 75 \text{ per year} \]\[ P = 1725 - 3 \times 75 = \text{Rs. } 1500 \]\[ R = \frac{75 \times 100}{1500} = 5\% \]Working back three years from the first amount recovers the principal.

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61.

Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.

A.Rs. 7804
B.Rs. 8979
C.Rs. 8046
D.Rs. 9009

Answer: D

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The rate \( 15\tfrac{2}{5}\% \) is 15.4%, and nine months is \( \tfrac{3}{4} \) of a year.

\[ \text{SI} = \frac{78000 \times 15.4 \times 0.75}{100} \]

\[ = 780 \times 15.4 \times 0.75 = 780 \times 11.55 = \text{Rs. } 9009 \]

Leaving the period as 9 rather than \( \tfrac{9}{12} \) would inflate the answer twelvefold.

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62.

Simple interest at x% for x years will come out to be Rs x on a sum of Rs?

A.x
B.100/x
C.100/x2
D.100x

Answer: B

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Both the rate and the time are \( x \), and the interest is also \( x \).

\[ x = \frac{P \times x \times x}{100} = \frac{P x^{2}}{100} \]

Dividing both sides by \( x \):

\[ 1 = \frac{Px}{100} \quad\Longrightarrow\quad P = \frac{100}{x} \]

Only one power of \( x \) survives the cancellation, which is what separates \( \tfrac{100}{x} \) from \( \tfrac{100}{x^{2}} \).

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63.

What is the minimum number of years upon which SI on Rs 2600 at 6.67% interest rate will be in whole number?

Answer: B

Simple Interest =Principal * Rate * Time

Principal = 2600 Rs

Interest Rate = 6.67%

=> SI = 2600 * (20/3)*Time

SI of the number will be a whole number for the first time when time is three as denominator of rate is 3.

Hence time should be set to 3 years.

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64.

What time will be taken by an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A.2 years
B.1 years
C.3 years
D.4 years

Answer: A

P= Rs 900

Rate = 4.5*

SI= Rs 81

=> SI= Time*P*rate

calculating for rate,

=> Time= SI/rate*P

= 81/4.5%*900

=> 2 years

Thus, it will take 2 years to yield Rs 81.

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65.

Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?

A.Rs.1000
B.Rs.1100
C.Rs.1050
D.Rs.1200

Answer: A

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The period \( 2\tfrac{2}{5} \) years is 2.4 years, and Rs. 1120 is the amount.

\[ 1120 = P\left(1 + \frac{5 \times 2.4}{100}\right) = P(1.12) \]

\[ P = \text{Rs. } 1000 \]

The interest is Rs. 120, which is 12% of the principal - 5% a year for 2.4 years.

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66.

What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?

A.Rs.525
B.Rs.500
C.Rs.550
D.Rs.555

Answer: B

\[ \text{SI} = \frac{P \times R \times T}{100} \]

\[ 70 = \frac{P \times 3.5 \times 4}{100} = 0.14P \]

\[ P = \frac{70}{0.14} = \text{Rs. } 500 \]

Over four years at 3.5% the interest comes to 14% of the sum.

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67.

At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?

A.5%
B.3 1/2%
C.4%
D.5 1/2 %

Answer: C

\[ \text{SI} = \frac{P \times R \times T}{100} \]

\[ \text{SI} = 900 - 750 = \text{Rs. } 150 \]

\[ 150 = \frac{750 \times R \times 5}{100} = 37.5R \]

\[ R = 4\% \]

The Rs. 900 is the amount, so the principal must be subtracted first.

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68.

What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?

A.5%
B.6%
C.4 1/2%
D.3 1/2 %

Answer: A

\[ \text{SI} = \frac{P \times R \times T}{100} \]

\[ 160 = \frac{800 \times R \times 4}{100} = 32R \]

\[ R = 5\% \]

The Rs. 160 is 20% of the principal, spread over four years - 5% a year.

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69.

Find the simple interest on Rs.500 for 9 months at 6 paisa per month?

A.Rs.345
B.Rs.270
C.Rs.275
D.Rs.324

Answer: B

"6 paisa per month" means 6 paise on each rupee each month, or 6% per month.

\[ \text{SI} = 500 \times \frac{6}{100} \times 9 \]

\[ = 500 \times 0.06 \times 9 = \text{Rs. } 270 \]

The rate is already monthly, so the nine months are used directly - no conversion to years is needed.

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70.

A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?

A.3%
B.5%
C.6%
D.4%

Answer: B

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Under simple interest the yearly addition is constant, so the gap between the two amounts covers two years.

\[ 1875 - 1725 = 150 \text{ over 2 years} \quad\Longrightarrow\quad 75 \text{ per year} \]

\[ P = 1725 - 3 \times 75 = \text{Rs. } 1500 \]

\[ R = \frac{75 \times 100}{1500} = 5\% \]

Working back three years from the first amount recovers the principal.

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