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### Question 1

An investor puts an amount of Rs. 200 in a simple interest scheme. If it amounts to Rs. 254 in 3 years @9%, what would it had amounted to had the rate been 2% more?

### Question 2

The simple interest on a certain principal sum @4% for a period of 4 years is Rs. 768. What is the sum?

### Question 3

A sum of Rs. 1100 is lent in two parts. One at 8% p.a. and one at 3% p.a. What is the amount lent at 8% if the total simple interest at the end of 6 years is Rs. 258?

**A**

Rs. 200.

**B**

Rs. 300.

**C**

Rs. 250.

**D**

Rs. 400.

**Soln.**

**Ans: a**

Let the amount x be lent at r1% and remaining (P - x) at r2%, and let the sum of interests be I. Then, I = ${x × r_1 × 6}/100$ + ${(P - x) × r_2 × 6}/100$, which simplifies to 100I = 6 × ($x × (r_1 - r_2) + P × r_2$). Putting r_{1} = 8, r_{2} = 3, P = 1100, I = 258, we get x = Rs. 200.

### Question 4

A sum of Rs. 56160 is divided into three parts such that simple interest on these parts at 10% p.a. after 3, 17 and 15 years, respectively, is same. What is the amount of the smallest part?

**A**

Rs. 7200.

**B**

Rs. 7300.

**C**

Rs. 7100.

**D**

Rs. 7400.

**Soln.**

**Ans: a**

We should use the shortcut technique here. If r_{1}, t_{1}, r_{2}, t_{2} and r_{3}, t_{3} be the rates and times for three parts with same interest amount, then the three parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2} : 1/{r_3 t_3}$. In our case r_{1} = r_{2} = r_{3} = 10, which cancels, so the ratio is $1/t_1 : 1/t_2 : 1/t_3$. The product of denominators is 3 × 17 × 15 = 765. Thus, the three parts are in the ratio $255 : 45 : 51$. The parts are: 56160 × $51/{255 + 45 + 51}$, 56160 × $45/{255 + 45 + 51}$ and 56160 × $255/{255 + 45 + 51}$, which are 40800, 7200 and 8160. The smaller is Rs. 7200.

### Question 5

A certain amount is split into two parts. The first part is invested at 10% p.a. and the second at 3% p.a. What is the total amount if the total simple interest at the end of 4 years is Rs. 220, and if the amount invested at 10% is Rs. 700?

**A**

Rs. 200.

**B**

Rs. 300.

**C**

Rs. 250.

**D**

Rs. 400.

**Soln.**

**Ans: a**

Let the amount x be invested at r1% and remaining (P - x) at r2%, and let the sum of interests be I. Then, I = ${x × r_1 × 4}/100$ + ${(P - x) × r_2 × 4}/100$, which simplifies to 100I = 4 × ($x × (r_1 - r_2) + P × r_2$). Putting r_{1} = 10, r_{2} = 3, x = 700, I = 220, we get P = Rs. 200.

This Blog Post/Article "Simple Interest Quiz Set 009" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-01