# Simple Interest Quiz Set 013

### Question 1

Simple interest on a certain sum of money is \$1/2\$ of the sum for 20 years. What is the rate of interest?

A

2%.

B

3%.

C

5%.

D

4%.

Soln.
Ans: a

We know, I = PRT/100. If I = P/2, then \$1/2\$ = RT/100. So R = \$100/{2 × 20}\$ = 2%.

### Question 2

The interest on Rs. 1000 @7% for a certain number of days starting from Jan 1, 2001 is Rs. 14. How many days?

A

73 days.

B

74 days.

C

72 days.

D

75 days.

Soln.
Ans: a

We have r = 7%, P = 1000, I = 14, so t = \${100 × 14}/{1000 × 7}\$. 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 3

The interest on a certain principal sum is 4/81 times the sum. What is R, the rate of interest, if the time is R years?

A

\$2{2/9}\$%.

B

\$2{1/3}\$%.

C

\$2{4/9}\$%.

D

\$2{1/9}\$%.

Soln.
Ans: a

I = P × (4/81), so we can write P × (4/81) = P × (R/100) × R. Cancelling P and solving for R, we get, R = \$√{100 × 4/81}\$ = \$2{2/9}\$%.

### Question 4

The interest on Rs. 13000 @7% for a certain number of days starting from Jan 1, 1601 is Rs. 182. How many days?

A

73 days.

B

74 days.

C

72 days.

D

75 days.

Soln.
Ans: a

We have r = 7%, P = 13000, I = 182, so t = \${100 × 182}/{13000 × 7}\$. 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

An amount of Rs. 2143 is split into two parts. The first part is invested @7% for 2 years, and the second @2% for 7 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{1/14}\$.

C

\${13/14}\$.

D

\$1{1/7}\$.

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 (2 × 7) : (7 × 2) = 14 : 14, or same as 1. Please note that the answer is independent of the value of the total amount.