# Simple Interest Quiz Set 015

### Question 1

A certain amount is split into two parts. The first part is invested at 8% p.a. and the second at 5% p.a. What is the total amount if the total simple interest at the end of 3 years is Rs. 357, and if the amount invested at 8% is Rs. 1800?

A

Rs. 1300.

B

Rs. 1400.

C

Rs. 1200.

D

Rs. 1500.

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 r1 = 8, r2 = 5, x = 1800, I = 357, we get P = Rs. 1300.

### Question 2

The difference between simple interests on an amount @9% for 15 years and at 6% for 12 years is Rs. 189. What is the amount?

A

Rs. 300.

B

Rs. 400.

C

Rs. 200.

D

Rs. 500.

Soln.
Ans: a

The shortcut formula is P = ${\text"diff" × 100}/{r_1 × t_1 - r_2 × t_2}$. Putting r1 = 9, t1 = 15, r2 = 6, t2 = 12, diff = 189, we get P = Rs. 300.

### Question 3

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 4

The interest on Rs. 16000 @9% for a certain number of days starting from Jan 1, 2001 is Rs. 288. How many days?

A

73 days.

B

74 days.

C

72 days.

D

75 days.

Soln.
Ans: a

We have r = 9%, P = 16000, I = 288, so t = ${100 × 288}/{16000 × 9}$. We get t = 1/5. The given year is not a leap year. So it has 365 days. Since 365/5 = 73, the number of days is 73.

### Question 5

The simple interest on a certain principal sum @8% for a period of 6 years is Rs. 864. What is the sum?

A

Rs. 1800.

B

Rs. 1900.

C

Rs. 1700.

D

Rs. 2000.

Soln.
Ans: a

P = $(I × 100)/(R × T)$. Solving, we get P = $(864 × 100)/(8 × 6)$ = Rs. 1800.