# Simple Interest Quiz Set 007

### Question 1

The interest on a certain principal sum is 4/9 times the sum. What is R, the rate of interest, if the time is R years?

A

\$6{2/3}\$%.

B

7%.

C

\$7{1/3}\$%.

D

\$6{1/3}\$%.

Soln.
Ans: a

I = P × (4/9), so we can write P × (4/9) = P × (R/100) × R. Cancelling P and solving for R, we get, R = \$√{100 × 4/9}\$ = \$6{2/3}\$%.

### Question 2

A sum of Rs. 1540 is divided into two parts such that simple interest on these parts at 10% p.a. after 6 and 5 years, respectively, is same. What is the amount of the smaller part?

A

Rs. 700.

B

Rs. 800.

C

Rs. 600.

D

Rs. 900.

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: 1540 × \$5/{6 + 5}\$, and 1540 × \$6/{6 + 5}\$, which are 700 and 840. The smaller is Rs. 700.

### Question 3

A sum of Rs. 1300 is split into two parts. The first part is invested at 12% p.a. and the second at 4% p.a. What is the amount invested at 12% if the total simple interest at the end of 4 years is Rs. 368?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

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 × 4}/100\$ + \${(P - x) × r_2 × 4}/100\$, which simplifies to 100I = 4 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 12, r2 = 4, P = 1300, I = 368, we get x = Rs. 500.

### Question 4

An investor puts an amount of Rs. 3100 in a simple interest scheme. If the rate of interest is 9%, how long does he have to wait for getting an amount of Rs. 4216?

A

4 years.

B

5 years.

C

3 years.

D

6 years.

Soln.
Ans: a

The interest is I = 4216 - 3100 = 1116. So T = \$(I × 100)/(R × P)\$. Solving, we get T = \$(1116 × 100)/(9 × 3100)\$ = 4 years.

### Question 5

A sum of Rs. 1100 is lent in two parts. One at 13% p.a. and one at 6% p.a. What is the amount lent at 13% if the total simple interest at the end of 5 years is Rs. 715?

A

Rs. 1100.

B

Rs. 1200.

C

Rs. 1000.

D

Rs. 1300.

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 = 13, r2 = 6, P = 1100, I = 715, we get x = Rs. 1100. 