Simple Interest Quiz Set 002

Question 1

An amount of Rs. 2143 is split into two parts. The first part is invested @7% for 2 years, and the second @2% for 7 years. What is the ratio of the first part is to the second part if they yield the same amount of simple interest?

A

1.

B

\$1{1/14}\$.

C

\${13/14}\$.

D

\$1{1/7}\$.

Soln.
Ans: a

Let the amounts be x and y. We have x × r1 × t1 = y × r2 × t2. We can see that x : y is same as r2t2 : r1t1. The ratio is (2 × 7) : (7 × 2) = 14 : 14, or same as 1. Please note that the answer is independent of the value of the total amount.

Question 2

What is the interest on Rs. 12500 @2% for 73 days starting from Jan 1, 3201?

A

Rs. 50.

B

Rs. 150.

C

Rs. 100.

D

Rs. 250.

Soln.
Ans: a

The given year is not a leap year. So it has 365 days. Since 73 X 5 = 365, t = 1/5 year. We have r = 2%, t = 1/5, P = 12500, so I = \${12500 × 2 × 1}/{5 × 100}\$ = Rs. 50.

Question 3

What is the interest on Rs. 9500 @2% for 73 days starting from Jan 1, 2201?

A

Rs. 38.

B

Rs. 138.

C

Rs. 88.

D

Rs. 238.

Soln.
Ans: a

The given year is not a leap year. So it has 365 days. Since 73 X 5 = 365, t = 1/5 year. We have r = 2%, t = 1/5, P = 9500, so I = \${9500 × 2 × 1}/{5 × 100}\$ = Rs. 38.

Question 4

A certain amount is split into two parts. The first part is invested at 11% p.a. and the second at 6% p.a. What is the total amount if the total simple interest at the end of 3 years is Rs. 246, and if the amount invested at 11% is Rs. 800?

A

Rs. 700.

B

Rs. 800.

C

Rs. 600.

D

Rs. 900.

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 × 3}/100\$ + \${(P - x) × r_2 × 3}/100\$, which simplifies to 100I = 3 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 11, r2 = 6, x = 800, I = 246, we get P = Rs. 700.

Question 5

The interest on a certain principal sum is 1/4 times the sum. What is R, the rate of interest, if the time is R years?

A

5%.

B

\$5{1/2}\$%.

C

6%.

D

\$4{1/2}\$%.

Soln.
Ans: a

I = P × (1/4), so we can write P × (1/4) = P × (R/100) × R. Cancelling P and solving for R, we get, R = \$√{100 × 1/4}\$ = 5%.