# Simple Interest Quiz Set 004

### Question 1

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 2

An amount of Rs. 2143 is split into two parts. The first part is invested @3% for 5 years, and the second @5% for 3 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{1/15}\$.

C

\${14/15}\$.

D

\$1{2/15}\$.

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 (5 × 3) : (3 × 5) = 15 : 15, or same as 1. Please note that the answer is independent of the value of the total amount.

### Question 3

A sum of Rs. 23650 is divided into three parts such that simple interest on these parts at 10% p.a. after 4, 7 and 17 years, respectively, is same. What is the amount of the smallest part?

A

Rs. 3080.

B

Rs. 3180.

C

Rs. 2980.

D

Rs. 3280.

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 4 × 7 × 17 = 476. Thus, the three parts are in the ratio \$119 : 68 : 28\$. The parts are: 23650 × \$28/{119 + 68 + 28}\$, 23650 × \$68/{119 + 68 + 28}\$ and 23650 × \$119/{119 + 68 + 28}\$, which are 13090, 7480 and 3080. The smaller is Rs. 3080.

### Question 4

The simple interest on a hypothetical investment is Rs. 5120. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

A

Rs. 80.

B

Rs. 180.

C

Rs. 130.

D

Rs. 280.

Soln.
Ans: a

If I is the interest, and principal is P, time is P, and rate is P, then, I = \$(P × P × P)/100\$. Which gives P = \$√^3{100 × I}\$, which is \$√^3{100 × 5120}\$, which is \$√^3{1000 × 8 × 8 × 8}\$ = Rs. 80.

### 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%. 