# Simple Interest Quiz Set 016

### Question 1

Mr. X puts an amount of Rs. 4100 in a simple interest scheme. If he gets a total amount of Rs. 4510 after 5 months, what is the rate of interest?

A

\${1/6}\$% p.a.

B

2% p.a.

C

\${1/3}\$% p.a.

D

\${5/12}\$% p.a.

Soln.
Ans: a

The interest is I = 4510 - 4100 = 410. So R = \$(I × 100)/(T × P)\$. Solving, we get R = \$(410 × 100)/(5 × 4100)\$ = 2% per month, which is \${1/6}\$% per annum. Please note that since the time is in months the rate is also p.m.

### Question 2

An amount of Rs. 1000 is split into two parts. The first part is invested @2% for 6 years, and the second @8% for 14 years. What is the ratio of the first part is to the second part if they yield the same amount of simple interest?

A

\$9{1/3}\$.

B

\$9{5/12}\$.

C

\$9{1/4}\$.

D

\$9{1/2}\$.

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 (8 × 14) : (2 × 6) = 112 : 12, or same as \$9{1/3}\$. Please note that the answer is independent of the value of the total amount.

### Question 3

Mr. X borrowed Rs. 900 from Mr. Y on simple interest @2% for 19 years. He then adds an amount x to it and lends it to Mr. Z @11% for the same duration. What is x if he gains Rs. 2584?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

Soln.
Ans: a

His gain is \${(900 + x) × 11 × 19}/100\$ - \${900 × 2 × 19}/100\$ = 2584. We can solve this for x to get x = Rs. 500.

### Question 4

The interest on a certain principal sum is 1/16 times the sum. What is R, the rate of interest, if the time is R years?

A

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

B

\$2{3/4}\$%.

C

3%.

D

\$2{1/4}\$%.

Soln.
Ans: a

I = P × (1/16), so we can write P × (1/16) = P × (R/100) × R. Cancelling P and solving for R, we get, R = \$√{100 × 1/16}\$ = \$2{1/2}\$%.

### Question 5

What is the interest on Rs. 12500 @6% for 73 days starting from Jan 1, 2601?

A

Rs. 150.

B

Rs. 250.

C

Rs. 200.

D

Rs. 350.

Soln.
Ans: a

The given year is not a leap year. So it has 365 days. Since 73 X 5 = 365, t = 1/5 year. We have r = 6%, t = 1/5, P = 12500, so I = \${12500 × 6 × 1}/{5 × 100}\$ = Rs. 150. 