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### Question 1

A sum of Rs. 24160 is divided into three parts such that simple interest on these parts at 10% p.a. after 11, 18 and 14 years, respectively, is same. What is the amount of the smallest part?

**A**

Rs. 6160.

**B**

Rs. 6260.

**C**

Rs. 6060.

**D**

Rs. 6360.

**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 11 × 18 × 14 = 2772. Thus, the three parts are in the ratio $252 : 154 : 198$. The parts are: 24160 × $198/{252 + 154 + 198}$, 24160 × $154/{252 + 154 + 198}$ and 24160 × $252/{252 + 154 + 198}$, which are 10080, 6160 and 7920. The smaller is Rs. 6160.

### Question 2

The difference between simple interests on an amount @8% for 22 years and at 5% for 17 years is Rs. 182. What is the amount?

### Question 3

The difference between simple interests on an amount @11% for 18 years and at 6% for 16 years is Rs. 816. What is the amount?

### Question 4

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 5

A sum of Rs. 1100 is divided into two parts such that simple interest on these parts at 10% p.a. after 6 and 5 years, respectively, is same. What is the amount of the smaller part?

**A**

Rs. 500.

**B**

Rs. 600.

**C**

Rs. 400.

**D**

Rs. 700.

**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: 1100 × $5/{6 + 5}$, and 1100 × $6/{6 + 5}$, which are 500 and 600. The smaller is Rs. 500.

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This Blog Post/Article "Simple Interest Quiz Set 017" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-01-21. Published on: 2016-05-01