# Simple Interest Quiz Set 003

### Question 1

An amount of Rs. 2143 is split into two parts. The first part is invested @10% for 4 years, and the second @4% for 10 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{1/40}\$.

C

\${39/40}\$.

D

\$1{1/20}\$.

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 (4 × 10) : (10 × 4) = 40 : 40, or same as 1. Please note that the answer is independent of the value of the total amount.

### Question 2

What is the interest on Rs. 9500 @2% for 73 days starting from Jan 1, 2201?

A

Rs. 38.

B

Rs. 138.

C

Rs. 88.

D

Rs. 238.

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 = 2%, t = 1/5, P = 9500, so I = \${9500 × 2 × 1}/{5 × 100}\$ = Rs. 38.

### Question 3

A sum of Rs. 1900 is split into two parts. The first part is invested at 8% p.a. and the second at 6% p.a. What is the amount invested at 8% if the total simple interest at the end of 5 years is Rs. 620?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

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 × 5}/100\$ + \${(P - x) × r_2 × 5}/100\$, which simplifies to 100I = 5 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 8, r2 = 6, P = 1900, I = 620, we get x = Rs. 500.

### Question 4

The simple interest on a certain principal sum @2% for a period of 4 years is Rs. 360. What is the sum?

A

Rs. 4500.

B

Rs. 4600.

C

Rs. 4400.

D

Rs. 4700.

Soln.
Ans: a

P = \$(I × 100)/(R × T)\$. Solving, we get P = \$(360 × 100)/(2 × 4)\$ = Rs. 4500.

### Question 5

An amount of Rs. 2143 is split into two parts. The first part is invested @17% for 4 years, and the second @4% for 17 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{1/68}\$.

C

\${67/68}\$.

D

\$1{1/34}\$.

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 (4 × 17) : (17 × 4) = 68 : 68, or same as 1. Please note that the answer is independent of the value of the total amount. 