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### Question 1

A certain amount is split into two parts. The first part is invested at 11% p.a. and the second at 6% p.a. What is the total amount if the total simple interest at the end of 3 years is Rs. 246, and if the amount invested at 11% is Rs. 800?

**A**

Rs. 700.

**B**

Rs. 800.

**C**

Rs. 600.

**D**

Rs. 900.

**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 = ${x × r_1 × 3}/100$ + ${(P - x) × r_2 × 3}/100$, which simplifies to 100I = 3 × ($x × (r_1 - r_2) + P × r_2$). Putting r_{1} = 11, r_{2} = 6, x = 800, I = 246, we get P = Rs. 700.

### Question 2

An amount of Rs. 2143 is split into two parts. The first part is invested @3% for 5 years, and the second @5% for 3 years. What is the ratio of the first part is to the second part if they yield the same amount of simple interest?

**A**

1.

**B**

$1{1/15}$.

**C**

${14/15}$.

**D**

$1{2/15}$.

**Soln.**

**Ans: a**

Let the amounts be x and y. We have x × r_{1} × t_{1} = y × r_{2} × t_{2}. We can see that x : y is same as r_{2}t_{2} : r_{1}t_{1}. The ratio is (5 × 3) : (3 × 5) = 15 : 15, or same as 1. *Please note that the answer is independent of the value of the total amount.*

### Question 3

A sum of Rs. 23650 is divided into three parts such that simple interest on these parts at 10% p.a. after 4, 7 and 17 years, respectively, is same. What is the amount of the smallest part?

**A**

Rs. 3080.

**B**

Rs. 3180.

**C**

Rs. 2980.

**D**

Rs. 3280.

**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 4 × 7 × 17 = 476. Thus, the three parts are in the ratio $119 : 68 : 28$. The parts are: 23650 × $28/{119 + 68 + 28}$, 23650 × $68/{119 + 68 + 28}$ and 23650 × $119/{119 + 68 + 28}$, which are 13090, 7480 and 3080. The smaller is Rs. 3080.

### Question 4

The simple interest on a hypothetical investment is Rs. 5120. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

### Question 5

The interest on a certain principal sum is 1/4 times the sum. What is R, the rate of interest, if the time is R years?

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