# Simple Interest Quiz Set 019

### Question 1

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 2

An investor puts an amount of Rs. 1600 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. 2080?

A

\${5/12}\$ year.

B

\${1/2}\$ year.

C

\${7/12}\$ year.

D

\${2/3}\$ year.

Soln.
Ans: a

The interest is I = 2080 - 1600 = 480. So T = \$(I × 100)/(R × P)\$. Solving, we get T = \$(480 × 100)/(6 × 1600)\$ = 5 months.

### Question 3

There are two simple interest investment options I and II. The rate of interest in option I is \${5/8}\$ times the rate for option II. The time period in option I is 8 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 × \${5/8} × {R/100}\$ × 8 × T. The ratio I1 to I2 is \$5/8\$ × 8 = 5.

### Question 4

A sum of Rs. 300 is lent in two parts. One at 10% p.a. and one at 3% p.a. What is the amount lent at 10% if the total simple interest at the end of 3 years is Rs. 300?

A

Rs. 1300.

B

Rs. 1400.

C

Rs. 1200.

D

Rs. 1500.

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 × 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 = 3, P = 300, I = 300, we get x = Rs. 1300.

### Question 5

A sum of Rs. 500 is lent in two parts. One at 9% p.a. and one at 4% p.a. What is the amount lent at 9% if the total simple interest at the end of 4 years is Rs. 120?

A

Rs. 200.

B

Rs. 300.

C

Rs. 250.

D

Rs. 400.

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 × 4}/100\$ + \${(P - x) × r_2 × 4}/100\$, which simplifies to 100I = 4 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 9, r2 = 4, P = 500, I = 120, we get x = Rs. 200. 