# Simple Interest Quiz Set 011

### Question 1

Mr. X puts an amount of Rs. 2600 in a simple interest scheme. If he gets a total amount of Rs. 3770 after 5 months, what is the rate of interest?

A

\${3/4}\$% p.a.

B

9% p.a.

C

\${11/12}\$% p.a.

D

1% p.a.

Soln.
Ans: a

The interest is I = 3770 - 2600 = 1170. So R = \$(I × 100)/(T × P)\$. Solving, we get R = \$(1170 × 100)/(5 × 2600)\$ = 9% per month, which is \${3/4}\$% per annum. Please note that since the time is in months the rate is also p.m.

### Question 2

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 3

The simple interest on a hypothetical investment is Rs. 5120. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

A

Rs. 80.

B

Rs. 180.

C

Rs. 130.

D

Rs. 280.

Soln.
Ans: a

If I is the interest, and principal is P, time is P, and rate is P, then, I = \$(P × P × P)/100\$. Which gives P = \$√^3{100 × I}\$, which is \$√^3{100 × 5120}\$, which is \$√^3{1000 × 8 × 8 × 8}\$ = Rs. 80.

### Question 4

A sum of Rs. 1300 is split into two parts. The first part is invested at 10% p.a. and the second at 5% p.a. What is the amount invested at 10% if the total simple interest at the end of 3 years is Rs. 375?

A

Rs. 1200.

B

Rs. 1300.

C

Rs. 1100.

D

Rs. 1400.

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 = 10, r2 = 5, P = 1300, I = 375, we get x = Rs. 1200.

### Question 5

An amount of Rs. 1000 is split into two parts. The first part is invested @5% for 6 years, and the second @7% for 8 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{13/15}\$.

B

\$1{9/10}\$.

C

\$1{5/6}\$.

D

\$1{14/15}\$.

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 (7 × 8) : (5 × 6) = 56 : 30, or same as \$1{13/15}\$. Please note that the answer is independent of the value of the total amount. 