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### Question 1

A sum of Rs. 500 is lent in two parts. One at 9% p.a. and one at 4% p.a. What is the amount lent at 9% if the total simple interest at the end of 4 years is Rs. 120?

**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 = ${x × r_1 × 4}/100$ + ${(P - x) × r_2 × 4}/100$, which simplifies to 100I = 4 × ($x × (r_1 - r_2) + P × r_2$). Putting r_{1} = 9, r_{2} = 4, P = 500, I = 120, we get x = Rs. 200.

### Question 2

The interest on Rs. 16000 @9% for a certain number of days starting from Jan 1, 2001 is Rs. 288. How many days?

### Question 3

A sum of Rs. 34300 is divided into three parts such that simple interest on these parts at 10% p.a. after 5, 11 and 18 years, respectively, is same. What is the amount of the smallest part?

**A**

Rs. 5500.

**B**

Rs. 5600.

**C**

Rs. 5400.

**D**

Rs. 5700.

**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 5 × 11 × 18 = 990. Thus, the three parts are in the ratio $198 : 90 : 55$. The parts are: 34300 × $55/{198 + 90 + 55}$, 34300 × $90/{198 + 90 + 55}$ and 34300 × $198/{198 + 90 + 55}$, which are 19800, 9000 and 5500. The smaller is Rs. 5500.

### Question 4

An investor puts an amount of Rs. 3100 in a simple interest scheme. If the rate of interest is 9%, how long does he have to wait for getting an amount of Rs. 4216?

### Question 5

A sum of Rs. 1540 is divided into two parts such that simple interest on these parts at 10% p.a. after 2 and 9 years, respectively, is same. What is the amount of the smaller part?

**A**

Rs. 280.

**B**

Rs. 380.

**C**

Rs. 180.

**D**

Rs. 480.

**Soln.**

**Ans: a**

We should use the shortcut technique here. If r_{1}, t_{1}, r_{2}, t_{2} be the rates and times for two parts with same interest amount, then the two parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2}$. In our case r_{1} = r_{2} = 10, which cancels, so the ratio is $1/t_1 : 1/t_2$. Thus, the two parts are in the ratio $t_2 : t_1$. The parts are: 1540 × $9/{2 + 9}$, and 1540 × $2/{2 + 9}$, which are 1260 and 280. The smaller is Rs. 280.

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This Blog Post/Article "Simple Interest Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-04-07.