Simple Interest Quiz Set 010

Question 1

Simple interest on a certain sum of money is \$1/4\$ of the sum for 5 years. What is the rate of interest?

A

5%.

B

6%.

C

4%.

D

7%.

Soln.
Ans: a

We know, I = PRT/100. If I = P/4, then \$1/4\$ = RT/100. So R = \$100/{4 × 5}\$ = 5%.

Question 2

A sum of Rs. 57970 is divided into three parts such that simple interest on these parts at 10% p.a. after 13, 17 and 4 years, respectively, is same. What is the amount of the smallest part?

A

Rs. 8840.

B

Rs. 8940.

C

Rs. 8740.

D

Rs. 9040.

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 13 × 17 × 4 = 884. Thus, the three parts are in the ratio \$68 : 52 : 221\$. The parts are: 57970 × \$221/{68 + 52 + 221}\$, 57970 × \$52/{68 + 52 + 221}\$ and 57970 × \$68/{68 + 52 + 221}\$, which are 11560, 8840 and 37570. The smaller is Rs. 8840.

Question 3

A sum of Rs. 3420 is divided into two parts such that simple interest on these parts at 10% p.a. after 12 and 7 years, respectively, is same. What is the amount of the smaller part?

A

Rs. 1260.

B

Rs. 1360.

C

Rs. 1160.

D

Rs. 1460.

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: 3420 × \$7/{12 + 7}\$, and 3420 × \$12/{12 + 7}\$, which are 1260 and 2160. The smaller is Rs. 1260.

Question 4

A sum of Rs. 1100 is split into two parts. The first part is invested at 12% p.a. and the second at 6% p.a. What is the amount invested at 12% if the total simple interest at the end of 5 years is Rs. 510?

A

Rs. 600.

B

Rs. 700.

C

Rs. 500.

D

Rs. 800.

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 × 5}/100\$ + \${(P - x) × r_2 × 5}/100\$, which simplifies to 100I = 5 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 12, r2 = 6, P = 1100, I = 510, we get x = Rs. 600.

Question 5

An investor puts an amount of Rs. 4200 in a simple interest scheme. If it amounts to Rs. 6258 in 7 years @7%, what would it had amounted to had the rate been 2% more?

A

Rs. 6846.

B

Rs. 6946.

C

Rs. 6746.

D

Rs. 7046.

Soln.
Ans: a

Shortcut is required here. The addition would be same as if R = 2%, T = 7 years and P = Rs. 4200, which is \${4200 × 2 × 7}/100\$ = 588. So new amount is 6258 + 588 = Rs. 6846. 