# Simple Interest Quiz Set 008

### Question 1

An investor puts an amount of Rs. 3200 in a simple interest scheme. If it amounts to Rs. 4640 in 9 years @5%, what would it had amounted to had the rate been 2% more?

A

Rs. 5216.

B

Rs. 5316.

C

Rs. 5116.

D

Rs. 5416.

Soln.
Ans: a

Shortcut is required here. The addition would be same as if R = 2%, T = 9 years and P = Rs. 3200, which is \${3200 × 2 × 9}/100\$ = 576. So new amount is 4640 + 576 = Rs. 5216.

### Question 2

A sum of Rs. 1200 is split into two parts. The first part is invested at 9% p.a. and the second at 4% p.a. What is the amount invested at 9% if the total simple interest at the end of 6 years is Rs. 558?

A

Rs. 900.

B

Rs. 1000.

C

Rs. 800.

D

Rs. 1100.

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 × 6}/100\$ + \${(P - x) × r_2 × 6}/100\$, which simplifies to 100I = 6 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 9, r2 = 4, P = 1200, I = 558, we get x = Rs. 900.

### Question 3

Mr. X borrowed Rs. 1500 from Mr. Y on simple interest @4% for 19 years. He then adds an amount x to it and lends it to Mr. Z @8% for the same duration. What is x if he gains Rs. 2052?

A

Rs. 600.

B

Rs. 700.

C

Rs. 500.

D

Rs. 800.

Soln.
Ans: a

His gain is \${(1500 + x) × 8 × 19}/100\$ - \${1500 × 4 × 19}/100\$ = 2052. We can solve this for x to get x = Rs. 600.

### Question 4

A sum of Rs. 34300 is divided into three parts such that simple interest on these parts at 10% p.a. after 5, 11 and 18 years, respectively, is same. What is the amount of the smallest part?

A

Rs. 5500.

B

Rs. 5600.

C

Rs. 5400.

D

Rs. 5700.

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 5 × 11 × 18 = 990. Thus, the three parts are in the ratio \$198 : 90 : 55\$. The parts are: 34300 × \$55/{198 + 90 + 55}\$, 34300 × \$90/{198 + 90 + 55}\$ and 34300 × \$198/{198 + 90 + 55}\$, which are 19800, 9000 and 5500. The smaller is Rs. 5500.

### Question 5

The simple interest on a hypothetical investment is Rs. 3430. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

A

Rs. 70.

B

Rs. 170.

C

Rs. 120.

D

Rs. 270.

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 × 3430}\$, which is \$√^3{1000 × 7 × 7 × 7}\$ = Rs. 70.