# Simple Interest Quiz Set 009

### Question 1

An investor puts an amount of Rs. 200 in a simple interest scheme. If it amounts to Rs. 254 in 3 years @9%, what would it had amounted to had the rate been 2% more?

A

Rs. 266.

B

Rs. 366.

C

Rs. 166.

D

Rs. 466.

Soln.
Ans: a

Shortcut is required here. The addition would be same as if R = 2%, T = 3 years and P = Rs. 200, which is \${200 × 2 × 3}/100\$ = 12. So new amount is 254 + 12 = Rs. 266.

### Question 2

The simple interest on a certain principal sum @4% for a period of 4 years is Rs. 768. What is the sum?

A

Rs. 4800.

B

Rs. 4900.

C

Rs. 4700.

D

Rs. 5000.

Soln.
Ans: a

P = \$(I × 100)/(R × T)\$. Solving, we get P = \$(768 × 100)/(4 × 4)\$ = Rs. 4800.

### Question 3

A sum of Rs. 1100 is lent in two parts. One at 8% p.a. and one at 3% p.a. What is the amount lent at 8% if the total simple interest at the end of 6 years is Rs. 258?

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 × 6}/100\$ + \${(P - x) × r_2 × 6}/100\$, which simplifies to 100I = 6 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 8, r2 = 3, P = 1100, I = 258, we get x = Rs. 200.

### Question 4

A sum of Rs. 56160 is divided into three parts such that simple interest on these parts at 10% p.a. after 3, 17 and 15 years, respectively, is same. What is the amount of the smallest part?

A

Rs. 7200.

B

Rs. 7300.

C

Rs. 7100.

D

Rs. 7400.

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 3 × 17 × 15 = 765. Thus, the three parts are in the ratio \$255 : 45 : 51\$. The parts are: 56160 × \$51/{255 + 45 + 51}\$, 56160 × \$45/{255 + 45 + 51}\$ and 56160 × \$255/{255 + 45 + 51}\$, which are 40800, 7200 and 8160. The smaller is Rs. 7200.

### Question 5

A certain amount is split into two parts. The first part is invested at 10% p.a. and the second at 3% p.a. What is the total amount if the total simple interest at the end of 4 years is Rs. 220, and if the amount invested at 10% is Rs. 700?

A

Rs. 200.

B

Rs. 300.

C

Rs. 250.

D

Rs. 400.

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 = 10, r2 = 3, x = 700, I = 220, we get P = Rs. 200. 