# Simple Interest Quiz Set 004

### Question 1

A sum of Rs. 270 is divided into two parts such that simple interest on these parts at 10% p.a. after 1 and 2 years, respectively, is same. What is the amount of the smaller part?

A

Rs. 90.

B

Rs. 190.

C

Rs. 140.

D

Rs. 290.

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: 270 × \$2/{1 + 2}\$, and 270 × \$1/{1 + 2}\$, which are 180 and 90. The smaller is Rs. 90.

### Question 2

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.

### Question 3

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 4

What is the interest on Rs. 12500 @6% for 73 days starting from Jan 1, 2601?

A

Rs. 150.

B

Rs. 250.

C

Rs. 200.

D

Rs. 350.

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 = 6%, t = 1/5, P = 12500, so I = \${12500 × 6 × 1}/{5 × 100}\$ = Rs. 150.

### Question 5

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}\$%.