# Simple Interest Quiz Set 003

### Question 1

A sum of Rs. 1540 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. 700.

B

Rs. 800.

C

Rs. 600.

D

Rs. 900.

Soln.
Ans: a

We should use the shortcut technique here. If r1, t1, r2, t2 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 r1 = r2 = 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 × $5/{6 + 5}$, and 1540 × $6/{6 + 5}$, which are 700 and 840. The smaller is Rs. 700.

### Question 2

An amount of Rs. 1000 is split into two parts. The first part is invested @2% for 3 years, and the second @10% for 6 years. What is the ratio of the first part is to the second part if they yield the same amount of simple interest?

A

10.

B

$10{1/6}$.

C

$9{5/6}$.

D

$10{1/3}$.

Soln.
Ans: a

Let the amounts be x and y. We have x × r1 × t1 = y × r2 × t2. We can see that x : y is same as r2t2 : r1t1. The ratio is (10 × 6) : (2 × 3) = 60 : 6, or same as 10. Please note that the answer is independent of the value of the total amount.

### Question 3

An investor puts an amount of Rs. 2500 in a simple interest scheme. If the rate of interest is 3%, how long does he have to wait for getting an amount of Rs. 3100?

A

8 years.

B

9 years.

C

7 years.

D

10 years.

Soln.
Ans: a

The interest is I = 3100 - 2500 = 600. So T = $(I × 100)/(R × P)$. Solving, we get T = $(600 × 100)/(3 × 2500)$ = 8 years.

### Question 4

The simple interest on a certain principal sum @4% for a period of 4 years is Rs. 768. What is the sum?

A

Rs. 4800.

B

Rs. 4900.

C

Rs. 4700.

D

Rs. 5000.

Soln.
Ans: a

P = $(I × 100)/(R × T)$. Solving, we get P = $(768 × 100)/(4 × 4)$ = Rs. 4800.

### Question 5

The difference between simple interests on an amount @11% for 6 years and at 4% for 13 years is Rs. 126. What is the amount?

A

Rs. 900.

B

Rs. 1000.

C

Rs. 800.

D

Rs. 1100.

Soln.
Ans: a

The shortcut formula is P = ${\text"diff" × 100}/{r_1 × t_1 - r_2 × t_2}$. Putting r1 = 11, t1 = 6, r2 = 4, t2 = 13, diff = 126, we get P = Rs. 900.