# Simple Interest Quiz Set 015

### Question 1

Simple interest on a certain sum of money is \$1/5\$ of the sum for 5 years. What is the rate of interest?

A

4%.

B

5%.

C

3%.

D

6%.

Soln.
Ans: a

We know, I = PRT/100. If I = P/5, then \$1/5\$ = RT/100. So R = \$100/{5 × 5}\$ = 4%.

### Question 2

A sum of Rs. 23650 is divided into three parts such that simple interest on these parts at 10% p.a. after 4, 7 and 17 years, respectively, is same. What is the amount of the smallest part?

A

Rs. 3080.

B

Rs. 3180.

C

Rs. 2980.

D

Rs. 3280.

Soln.
Ans: a

We should use the shortcut technique here. If r1, t1, r2, t2 and r3, t3 be the rates and times for three parts with same interest amount, then the three parts must be in the ratio \$1/{r_1 t_1} : 1/{r_2 t_2} : 1/{r_3 t_3}\$. In our case r1 = r2 = r3 = 10, which cancels, so the ratio is \$1/t_1 : 1/t_2 : 1/t_3\$. The product of denominators is 4 × 7 × 17 = 476. Thus, the three parts are in the ratio \$119 : 68 : 28\$. The parts are: 23650 × \$28/{119 + 68 + 28}\$, 23650 × \$68/{119 + 68 + 28}\$ and 23650 × \$119/{119 + 68 + 28}\$, which are 13090, 7480 and 3080. The smaller is Rs. 3080.

### Question 3

An investor puts an amount of Rs. 900 in a simple interest scheme. If the rate of interest is 5% per month, how long does he have to wait for getting an amount of Rs. 1035?

A

\${1/4}\$ year.

B

\${1/3}\$ year.

C

\${5/12}\$ year.

D

\${1/2}\$ year.

Soln.
Ans: a

The interest is I = 1035 - 900 = 135. So T = \$(I × 100)/(R × P)\$. Solving, we get T = \$(135 × 100)/(5 × 900)\$ = 3 months.

### Question 4

Mr. X borrowed Rs. 1800 from Mr. Y on simple interest @6% for 13 years. He then adds an amount x to it and lends it to Mr. Z @13% for the same duration. What is x if he gains Rs. 2483?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

Soln.
Ans: a

His gain is \${(1800 + x) × 13 × 13}/100\$ - \${1800 × 6 × 13}/100\$ = 2483. We can solve this for x to get x = Rs. 500.

### Question 5

The interest on Rs. 6000 @6% for a certain number of days starting from Jan 1, 1801 is Rs. 72. How many days?

A

73 days.

B

74 days.

C

72 days.

D

75 days.

Soln.
Ans: a

We have r = 6%, P = 6000, I = 72, so t = \${100 × 72}/{6000 × 6}\$. We get t = 1/5. The given year is not a leap year. So it has 365 days. Since 365/5 = 73, the number of days is 73.