# How To Solve Quickly Simple Interest Questions

## Definition of Simple Interest

If the interest on a sum borrowed for certain period is calculated uniformly, then it is called simple interest.

- It is simply obtained by multiplying principal amount with rate and with given time interval.
**Formula – SI=P*R*T/100**

For Example-What is simple interest of Rs 5000/- for 5 years at 5% interest per annum.

**Sol-** SI= P*R*T/100

= 5000*5*5/100

=Rs 1250.

## Type 1: To find the Simple Interest (SI)

### Question 1.

** Find the simple interest on Rs. 60,000 at 13/5 % p.a. for a period of 9 months?**

Options:

A. 1170

B. 1710

C. 11700

D. 1017

#### Solution:

We know that, SI = P*r*t/100

P = 60000

R = 13/5%

T = 9 months = 3/4th year

SI = (60000 *13/ 5 * 3/4)/100

SI = 117000/100

SI = 1170

#### Correct option: A

### Question 2.

**What will be the ratio of simple interest earned on a certain amount at the same rate of interest for 6 years and that for 24 years?**

Options:

A. 1:2

B. 3:5

C. 1:3

D. 1:4

#### Solution:

Required Ratio = Simple Interest for 6 years/Simple Interest for 24 years

=T_{1}/T_{2}

=6/24

=1/4

=1:4

#### Correct option: D

### Question 3.

**Find the simple interest on Rs.500 for 10 months at 5 paisa per month?**

Options:

A. Rs. 2500

B. Rs. 250

C. Rs. 25

D. Rs. 25.5

#### Solution:

SI = P*r*t/100

SI = (500*5*10)/100 = Rs. 250

#### Correct option: B

## Type 2: When Rates are different for different years

### Question 1.

**Nisha borrowed some money at the rate of 5% p.a. for the first two years. She again borrowed at the rate of 10% p.a. for the next three years. Later at the rate of 15% p.a. for the rest of the years. Total interest paid by her was Rs. 15000 at the end of 10 years. Calculate the amount of money she borrowed?**

Options:

A. Rs. 15005

B. Rs. 20000

C. Rs. 15000

D. Rs. 10000

#### Solution:

According to the question,

r_{1} = 5%, T_{1} = 2 years

r_{2} = 10%, T_{2} = 3 years

r_{3} = 15%, T_{3} = 5 years (since, beyond 5 years rate is 14%)

Simple interest = 15000

Therefore, P = (15000 x 100)/ (5*2 +10*3 +15*4)

= 1500000/ (10 + 30 + 60)

= 1500000/ 100

= Rs. 15000

#### Correct option: C

### Question 2.

**Rahul invests some amount of money in three different schemes for 5 years, 10 years and 15 years at 10%, 12% and 15% Simple Interest respectively. At the completion of each scheme, he gets the same interest. Find out the ratio of his investment?**

Options:

A. 3: 9: 15

B. 10: 24: 45

C. 10: 24: 40

D. 9: 24: 45

#### Solution:

If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are R_{1}, R_{2}, … , R_{n} respectively and time periods are T_{1}, T_{2}, … , T_{n} respectively, then the ratio in which the sum will be divided in n parts can be given by 1/R_{1}T_{1}: 1/R_{2}T_{2}: ..1/R_{n}T_{n}

Here, T_{1} = 5, T_{2} = 10 and T_{3} = 15 years

And, R_{1} = 9%, R_{2} = 12%, and R_{3} = 15% resp.

Hence, the ratio of his investment will be

100/50 : 100/120 : 100/225

10 : 24 : 45

**Correct option: B**

### Question 3.

**Ram tool a loan for Rs.10000 from bank for a period of 3 years. The bank charged the interest rates as 5% for first year, 7% for second year and 9% for the third year. Find the amount he has to pay back to the bank after three years?**

Options:

A. Rs. 18500

B. Rs. 145000

C. Rs. 15100

D. Rs 12100.

#### Solution:

Simple Interest = 5% + 7% + 9% = 21%.

Amount = Principal + Rate of Interest.

Principal is 100% of the amount.

Therefore, Amount = 100% + 21%.= 121%

According to the question,

100% 10000

121% A

By cross multiplication we get,

A = (121 * 10000)/100)

A = 12100

Therefore, the amount that Ram has to pay back to the bank after three years Rs 12100.

#### Correct option: D

## Type 3: To find the (Rate of Interest, Time period, Principal)

### Question 1.

** A sum of money becomes six times in 30 years. Calculate the rate of interest.**

Options:

A. 16.66%

B. 4.5%

C. 15.45%

D. 15%

#### Solution:

We know that, if sum of money becomes x times in n years at some rate of interest, then rate of interest is calculated as,

R = 100 (x-1)/n %

R = 100 (6 – 1)/30

R = 100 (5)/30

R = 500/30

R = 16.66%

#### Correct option: A

### Question 2.

** How much time will it take for an amount of Rs. 630 to yield Rs. 72 as interest at 5.4 % p.a. of simple interest?**

Options:

A. 2 years and 10 months

B. 1 years and 11 months

C. 2 years and 11 months

D. 1 years and 11 months

#### Solution:

We know that, Time = 100* SI/ R * P

T = (100 * 72)/630 * 5.4

T = 7200/3402

T = 2 years and 11 months

#### Correct option: C

### Question 3.

** Mr. Tata invested Rs. 13,900 in two different schemes I and II. The rate of interest for both the schemes were 14% and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme II?**

Options:

A. Rs. 2400

B. Rs. 6200

C. Rs. 6400

D. Rs. 4600

#### Solution:

Let the amount invested in schemes I = x

Therefore, in schemes II = 13900 – x

SI (scheme I) = P*r*t/100

Then For scheme I,

SI = x * 14 * 2/100

Then For scheme II,

SI (scheme II) = 13900-x * 14 * 2/100

SI (scheme I) + SI (scheme II) = 3508

x * 14 * 2/100 + 13900-x * 14 * 2/100 = 3508

28x/100 + (13900 – x) * 22/100 = 3508

6x = 45000

x = 45000/6

x = 7500

Hence, the sum invested in Scheme II = 13900 – 7500 = Rs. 6400

#### Correct option: C

- Read Also –
**Formulas to solve simple interest questions**

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