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### Question 1

A sum of Rs. 270 is divided into two parts such that simple interest on these parts at 10% p.a. after 1 and 2 years, respectively, is same. What is the amount of the smaller part?

**A**

Rs. 90.

**B**

Rs. 190.

**C**

Rs. 140.

**D**

Rs. 290.

**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: 270 × $2/{1 + 2}$, and 270 × $1/{1 + 2}$, which are 180 and 90. The smaller is Rs. 90.

### Question 2

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.

### Question 3

A sum of Rs. 57970 is divided into three parts such that simple interest on these parts at 10% p.a. after 13, 17 and 4 years, respectively, is same. What is the amount of the smallest part?

**A**

Rs. 8840.

**B**

Rs. 8940.

**C**

Rs. 8740.

**D**

Rs. 9040.

**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 13 × 17 × 4 = 884. Thus, the three parts are in the ratio $68 : 52 : 221$. The parts are: 57970 × $221/{68 + 52 + 221}$, 57970 × $52/{68 + 52 + 221}$ and 57970 × $68/{68 + 52 + 221}$, which are 11560, 8840 and 37570. The smaller is Rs. 8840.

### Question 4

What is the interest on Rs. 12500 @6% for 73 days starting from Jan 1, 2601?

### Question 5

The interest on a certain principal sum is 4/9 times the sum. What is R, the rate of interest, if the time is R years?

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This Blog Post/Article "Simple Interest Quiz Set 004" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-04-07.