# Simple Interest Quiz Set 005

### Question 1

There are two simple interest investment options I and II. The rate of interest in option I is \$1{1/2}\$ times the rate for option II. The time period in option I is 2 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

3.

B

4.

C

2.

D

6.

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 × \${3/2} × {R/100}\$ × 2 × T. The ratio I1 to I2 is \$3/2\$ × 2 = 3.

### 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. 4600 in a simple interest scheme. If the rate of interest is 8%, how long does he have to wait for getting an amount of Rs. 5336?

A

2 years.

B

3 years.

C

5 years.

D

4 years.

Soln.
Ans: a

The interest is I = 5336 - 4600 = 736. So T = \$(I × 100)/(R × P)\$. Solving, we get T = \$(736 × 100)/(8 × 4600)\$ = 2 years.

### Question 4

A sum of Rs. 3420 is divided into two parts such that simple interest on these parts at 10% p.a. after 12 and 7 years, respectively, is same. What is the amount of the smaller part?

A

Rs. 1260.

B

Rs. 1360.

C

Rs. 1160.

D

Rs. 1460.

Soln.
Ans: a

We should use the shortcut technique here. If r1, t1, r2, t2 be the rates and times for two parts with same interest amount, then the two parts must be in the ratio \$1/{r_1 t_1} : 1/{r_2 t_2}\$. In our case r1 = r2 = 10, which cancels, so the ratio is \$1/t_1 : 1/t_2\$. Thus, the two parts are in the ratio \$t_2 : t_1\$. The parts are: 3420 × \$7/{12 + 7}\$, and 3420 × \$12/{12 + 7}\$, which are 1260 and 2160. The smaller is Rs. 1260.

### Question 5

A sum of Rs. 1200 is split into two parts. The first part is invested at 9% p.a. and the second at 4% p.a. What is the amount invested at 9% if the total simple interest at the end of 6 years is Rs. 558?

A

Rs. 900.

B

Rs. 1000.

C

Rs. 800.

D

Rs. 1100.

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 × 6}/100\$ + \${(P - x) × r_2 × 6}/100\$, which simplifies to 100I = 6 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 9, r2 = 4, P = 1200, I = 558, we get x = Rs. 900.