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### Question 1

Simple interest on a certain sum of money is $1/4$ of the sum for 5 years. What is the rate of interest?

### Question 2

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 3

A sum of Rs. 3420 is divided into two parts such that simple interest on these parts at 10% p.a. after 12 and 7 years, respectively, is same. What is the amount of the smaller part?

**A**

Rs. 1260.

**B**

Rs. 1360.

**C**

Rs. 1160.

**D**

Rs. 1460.

**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: 3420 × $7/{12 + 7}$, and 3420 × $12/{12 + 7}$, which are 1260 and 2160. The smaller is Rs. 1260.

### Question 4

A sum of Rs. 1100 is split into two parts. The first part is invested at 12% p.a. and the second at 6% p.a. What is the amount invested at 12% if the total simple interest at the end of 5 years is Rs. 510?

**A**

Rs. 600.

**B**

Rs. 700.

**C**

Rs. 500.

**D**

Rs. 800.

**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 = ${x × r_1 × 5}/100$ + ${(P - x) × r_2 × 5}/100$, which simplifies to 100I = 5 × ($x × (r_1 - r_2) + P × r_2$). Putting r_{1} = 12, r_{2} = 6, P = 1100, I = 510, we get x = Rs. 600.

### Question 5

An investor puts an amount of Rs. 4200 in a simple interest scheme. If it amounts to Rs. 6258 in 7 years @7%, what would it had amounted to had the rate been 2% more?

This Blog Post/Article "Simple Interest Quiz Set 010" 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