# Simple Interest Quiz Set 005

### Question 1

A certain amount is split into two parts. The first part is invested at 10% p.a. and the second at 5% p.a. What is the total amount if the total simple interest at the end of 2 years is Rs. 240, and if the amount invested at 10% is Rs. 1400?

A

Rs. 1000.

B

Rs. 1100.

C

Rs. 900.

D

Rs. 1200.

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 × 2}/100\$ + \${(P - x) × r_2 × 2}/100\$, which simplifies to 100I = 2 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 10, r2 = 5, x = 1400, I = 240, we get P = Rs. 1000.

### Question 2

Mr. X puts an amount of Rs. 3900 in a simple interest scheme. If he gets a total amount of Rs. 5304 after 4 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 = 5304 - 3900 = 1404. So R = \$(I × 100)/(T × P)\$. Solving, we get R = \$(1404 × 100)/(4 × 3900)\$ = 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 3

An investor puts an amount of Rs. 1500 in a simple interest scheme. If the rate of interest is 2%, how long does he have to wait for getting an amount of Rs. 1560?

A

2 years.

B

3 years.

C

5 years.

D

4 years.

Soln.
Ans: a

The interest is I = 1560 - 1500 = 60. So T = \$(I × 100)/(R × P)\$. Solving, we get T = \$(60 × 100)/(2 × 1500)\$ = 2 years.

### Question 4

There are two simple interest investment options I and II. The rate of interest in option I is \${5/16}\$ times the rate for option II. The time period in option I is 16 times that for the option II. What is the ratio of interest of option I to option II, if the same amount is invested in either?

A

5.

B

6.

C

4.

D

8.

Soln.
Ans: a

Let P, R and T have their usual meanings. For option II we have I2 = PRT/100. For option I we have I1 = P × \${5/16} × {R/100}\$ × 16 × T. The ratio I1 to I2 is \$5/16\$ × 16 = 5.

### Question 5

Mr. X borrowed Rs. 1100 from Mr. Y on simple interest @6% for 6 years. He then adds an amount x to it and lends it to Mr. Z @9% for the same duration. What is x if he gains Rs. 414?

A

Rs. 400.

B

Rs. 500.

C

Rs. 300.

D

Rs. 600.

Soln.
Ans: a

His gain is \${(1100 + x) × 9 × 6}/100\$ - \${1100 × 6 × 6}/100\$ = 414. We can solve this for x to get x = Rs. 400. 