### Type 2: How to Solve Problems On Simple Interest (SI) 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 = \frac{1500 * 100}{5*2 +10*3 +15*4 }

=\frac{1500000}{10 + 30 + 60 }

= \frac{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, total amount to be paid

A =\frac{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**

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