# Simple Interest Quiz Set 014

### Question 1

The simple interest on a hypothetical investment is Rs. 1250. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

A

Rs. 50.

B

Rs. 150.

C

Rs. 100.

D

Rs. 250.

Soln.
Ans: a

If I is the interest, and principal is P, time is P, and rate is P, then, I = \$(P × P × P)/100\$. Which gives P = \$√^3{100 × I}\$, which is \$√^3{100 × 1250}\$, which is \$√^3{1000 × 5 × 5 × 5}\$ = Rs. 50.

### Question 2

An investor puts an amount of Rs. 1600 in a simple interest scheme. If it amounts to Rs. 1696 in 3 years @2%, what would it had amounted to had the rate been 2% more?

A

Rs. 1792.

B

Rs. 1892.

C

Rs. 1692.

D

Rs. 1992.

Soln.
Ans: a

Shortcut is required here. The addition would be same as if R = 2%, T = 3 years and P = Rs. 1600, which is \${1600 × 2 × 3}/100\$ = 96. So new amount is 1696 + 96 = Rs. 1792.

### Question 3

A sum of Rs. 300 is lent in two parts. One at 7% p.a. and one at 2% p.a. What is the amount lent at 7% if the total simple interest at the end of 5 years is Rs. 155?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

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 = 7, r2 = 2, P = 300, I = 155, we get x = Rs. 500.

### Question 4

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 5

The simple interest on a hypothetical investment is Rs. 80. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

A

Rs. 20.

B

Rs. 120.

C

Rs. 70.

D

Rs. 220.

Soln.
Ans: a

If I is the interest, and principal is P, time is P, and rate is P, then, I = \$(P × P × P)/100\$. Which gives P = \$√^3{100 × I}\$, which is \$√^3{100 × 80}\$, which is \$√^3{1000 × 2 × 2 × 2}\$ = Rs. 20. 