Simple Interest Questions and Answers

Q: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ \text{SI} = 920 - 800 = 120 \quad\Longrightarrow\quad 120 = \frac{800 \times R \times 3}{100} = 24R \]\[ R = 5\% \]At \( 5 + 3 = 8\% \):\[ \text{SI} = \frac{800 \times 8 \times 3}{100} = 192 \quad\Longrightarrow\quad \text{amount} = \text{Rs. } 992 \]The extra 3% over three years adds \( 800 \times 0.09 = 72 \) - the same answer in one step.

Q: Aman invests Rs. 8000 at some rate of interest. Being simple interest the money doubles in 5 years. Raj sees this and invests Rs. 6250 for 3 years at same rate of interest. How much interest does Raj get?

\[ \text{SI} = \frac{P \times R \times T}{100} \]Doubling means the interest equals the principal.\[ P = \frac{P \times R \times 5}{100} \quad\Longrightarrow\quad R = 20\% \]\[ \text{Raj's interest} = \frac{6250 \times 20 \times 3}{100} = \text{Rs. } 3750 \]Aman's Rs. 8000 never enters Raj's calculation; it serves only to fix the rate, and even that cancels out of the doubling condition.

Q: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?

Doubling in 8 years fixes the rate:\[ P = \frac{P \times R \times 8}{100} \quad\Longrightarrow\quad R = 12.5\% \]After 10 years:\[ \text{amount} = P\left(1 + \frac{12.5 \times 10}{100}\right) = P(1 + 1.25) = 2.25P \]So it becomes \( 2\tfrac{1}{4} \) times itself. Under simple interest the multiple grows linearly with time, so ten years gives \( \tfrac{10}{8} \) of the interest, not of the amount.

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: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ 16500 = \frac{5000 \times 15 \times T}{100} = 750\,T \]\[ T = \frac{16500}{750} = 22 \text{ years} \]The interest is more than three times the principal, so a long period is expected - at 15% a year it takes over six years just to match the sum.

Q: Suresh for 2 years invested Rs. 500 in SBI. He also invested Rs. 300 in ICICI for 4 years. At the end he received Rs. 220 from both banks as simple interest. What must have been rate of interest?

\[ \text{SI} = \frac{P \times R \times T}{100} \]The two deposits share one rate \( r \), so add their interests.\[ \frac{500 \times r \times 2}{100} + \frac{300 \times r \times 4}{100} = 220 \]\[ 10r + 12r = 220 \quad\Longrightarrow\quad 22r = 220 \]\[ r = 10\% \]Checking: Rs. 100 from SBI and Rs. 120 from ICICI.

Q: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

\[ \text{SI} = \frac{P \times R \times T}{100} \]With the sum and the rate the same, simple interest is proportional to time.\[ \frac{\text{SI}_{6}}{\text{SI}_{9}} = \frac{6}{9} = \frac{2}{3} \]So the ratio is \( 2 : 3 \). Neither the sum nor the rate is needed - both cancel - so "data inadequate" is a trap.

Q: Aman got a salary of Rs. 8600. The salary was invested by him in two parts. Find the difference between the two parts of his salary, if in first part he got some simple interest at 15% per annum in 4 years, which was same as the second part which he invested at 20% for 3 years.

\[ \text{SI} = \frac{P \times R \times T}{100} \]Set the two interests equal and see what it forces.\[ \frac{p_{1} \times 15 \times 4}{100} = \frac{p_{2} \times 20 \times 3}{100} \]\[ 0.6\,p_{1} = 0.6\,p_{2} \quad\Longrightarrow\quad p_{1} = p_{2} \]\[ \text{difference} = \text{Rs. } 0 \]Both products \( R \times T \) come to 60, so the two schemes are identical and the salary splits exactly in half - Rs. 4300 each.

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61.

Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?

A.Rs.1056
B.Rs.1112
C.Rs.1182
D.Rs.992

Answer: D

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

\[ \text{SI} = 920 - 800 = 120 \quad\Longrightarrow\quad 120 = \frac{800 \times R \times 3}{100} = 24R \]

\[ R = 5\% \]

At \( 5 + 3 = 8\% \):

\[ \text{SI} = \frac{800 \times 8 \times 3}{100} = 192 \quad\Longrightarrow\quad \text{amount} = \text{Rs. } 992 \]

The extra 3% over three years adds \( 800 \times 0.09 = 72 \) - the same answer in one step.

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62.

An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?

A.10%
B.10.25%
C.10.5%
D.None of these

Answer: B

Let the sum be Rs. 100. Then,

S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5

S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25

So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%.

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63.

Aman invests Rs. 8000 at some rate of interest. Being simple interest the money doubles in 5 years. Raj sees this and invests Rs. 6250 for 3 years at same rate of interest. How much interest does Raj get?

A.Rs. 3750
B.Rs. 6250
C.Rs. 3125
D.Rs. 4250

Answer: A

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

Doubling means the interest equals the principal.

\[ P = \frac{P \times R \times 5}{100} \quad\Longrightarrow\quad R = 20\% \]

\[ \text{Raj's interest} = \frac{6250 \times 20 \times 3}{100} = \text{Rs. } 3750 \]

Aman's Rs. 8000 never enters Raj's calculation; it serves only to fix the rate, and even that cancels out of the doubling condition.

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64.

A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?

A.2 1/4
B.4 1/4
C.5 1/4
D.None

Answer: A

Doubling in 8 years fixes the rate:

\[ P = \frac{P \times R \times 8}{100} \quad\Longrightarrow\quad R = 12.5\% \]

After 10 years:

\[ \text{amount} = P\left(1 + \frac{12.5 \times 10}{100}\right) = P(1 + 1.25) = 2.25P \]

So it becomes \( 2\tfrac{1}{4} \) times itself. Under simple interest the multiple grows linearly with time, so ten years gives \( \tfrac{10}{8} \) of the interest, not of the amount.

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65.

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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66.

In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?

A.22
B.24
C.25
D.23

Answer: A

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

\[ 16500 = \frac{5000 \times 15 \times T}{100} = 750\,T \]

\[ T = \frac{16500}{750} = 22 \text{ years} \]

The interest is more than three times the principal, so a long period is expected - at 15% a year it takes over six years just to match the sum.

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67.

Suresh for 2 years invested Rs. 500 in SBI. He also invested Rs. 300 in ICICI for 4 years. At the end he received Rs. 220 from both banks as simple interest. What must have been rate of interest?

A.10%
B.12%
C.11%
D.5.5%

Answer: A

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

The two deposits share one rate \( r \), so add their interests.

\[ \frac{500 \times r \times 2}{100} + \frac{300 \times r \times 4}{100} = 220 \]

\[ 10r + 12r = 220 \quad\Longrightarrow\quad 22r = 220 \]

\[ r = 10\% \]

Checking: Rs. 100 from SBI and Rs. 120 from ICICI.

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68.

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

A.1:3
B.1:4
C.2:3
D.Data inadequate

Answer: C

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

With the sum and the rate the same, simple interest is proportional to time.

\[ \frac{\text{SI}_{6}}{\text{SI}_{9}} = \frac{6}{9} = \frac{2}{3} \]

So the ratio is \( 2 : 3 \). Neither the sum nor the rate is needed - both cancel - so "data inadequate" is a trap.

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69.

Aman got a salary of Rs. 8600. The salary was invested by him in two parts. Find the difference between the two parts of his salary, if in first part he got some simple interest at 15% per annum in 4 years, which was same as the second part which he invested at 20% for 3 years.

A.Rs. 0
B.Rs. 2400
C.Rs. 100
D.Rs. 4500

Answer: A

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

Set the two interests equal and see what it forces.

\[ \frac{p_{1} \times 15 \times 4}{100} = \frac{p_{2} \times 20 \times 3}{100} \]

\[ 0.6\,p_{1} = 0.6\,p_{2} \quad\Longrightarrow\quad p_{1} = p_{2} \]

\[ \text{difference} = \text{Rs. } 0 \]

Both products \( R \times T \) come to 60, so the two schemes are identical and the salary splits exactly in half - Rs. 4300 each.

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70.

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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