# Simple Interest Quiz Set 006

### Question 1

There are two simple interest investment options I and II. The rate of interest in option I is \${4/11}\$ times the rate for option II. The time period in option I is 11 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

4.

B

5.

C

3.

D

7.

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 × \${4/11} × {R/100}\$ × 11 × T. The ratio I1 to I2 is \$4/11\$ × 11 = 4.

### Question 2

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 3

An investor puts an amount of Rs. 3000 in a simple interest scheme. If the rate of interest is 6% per month, how long does he have to wait for getting an amount of Rs. 4080?

A

\${1/2}\$ year.

B

\${7/12}\$ year.

C

\${2/3}\$ year.

D

\${3/4}\$ year.

Soln.
Ans: a

The interest is I = 4080 - 3000 = 1080. So T = \$(I × 100)/(R × P)\$. Solving, we get T = \$(1080 × 100)/(6 × 3000)\$ = 6 months.

### Question 4

A sum of Rs. 1100 is lent in two parts. One at 13% p.a. and one at 6% p.a. What is the amount lent at 13% if the total simple interest at the end of 5 years is Rs. 715?

A

Rs. 1100.

B

Rs. 1200.

C

Rs. 1000.

D

Rs. 1300.

Soln.
Ans: a

Let the amount x be lent 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 = 13, r2 = 6, P = 1100, I = 715, we get x = Rs. 1100.

### 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.