Simple Interest Quiz Set 011

Question 1

The difference between simple interests on an amount @7% for 17 years and at 2% for 6 years is Rs. 535. What is the amount?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

Soln.
Ans: a

The shortcut formula is P = ${\text"diff" × 100}/{r_1 × t_1 - r_2 × t_2}$. Putting r1 = 7, t1 = 17, r2 = 2, t2 = 6, diff = 535, we get P = Rs. 500.

Question 2

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 3

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 4

An amount of Rs. 1000 is split into two parts. The first part is invested @5% for 6 years, and the second @7% for 8 years. What is the ratio of the first part is to the second part if they yield the same amount of simple interest?

A

$1{13/15}$.

B

$1{9/10}$.

C

$1{5/6}$.

D

$1{14/15}$.

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 (7 × 8) : (5 × 6) = 56 : 30, or same as $1{13/15}$. Please note that the answer is independent of the value of the total amount.

Question 5

An investor puts an amount of Rs. 4500 in a simple interest scheme. If the rate of interest is 4% per month, how long does he have to wait for getting an amount of Rs. 5940?

A

${2/3}$ year.

B

${3/4}$ year.

C

${5/6}$ year.

D

${11/12}$ year.

Soln.
Ans: a

The interest is I = 5940 - 4500 = 1440. So T = $(I × 100)/(R × P)$. Solving, we get T = $(1440 × 100)/(4 × 4500)$ = 8 months.