Aptitude : Simple Interest

(11) A sum amounts to Rs. 7000 in 2 years and Rs. 7400 in 3 years. What is the principal?

• (a)6600 Rupees
• (b)4400 Rupees
• (c)5850 Rupees
• (d)6000 Rupees

Answer

Correct Answer : (a) 6600 Rupees
Simple Interest = (principal amount * rate of interest * time period) / 100
We know that the amount in 2 years is Rs. 7000, the amount in 3 years is Rs. 7400, and the time period is 1 year.
7400 = 7000 + (7000 * rate of interest * 1) / 100
400 = (7000 * rate of interest) / 100
rate of interest = 400/7000 = 0.057 = 5.7%
The principal amount can be calculated using the following formula:
principal amount = (amount in 2 years) – (interest earned in 1 year)
principal amount = 7000 – 400 = Rs. 6600
Therefore, the principal is Rs. 6600 and the rate of interest is 5.7%.

(12) If a certain sum of money becomes three times in 8 years at simple interest, find the rate of interest.

• (a)30 Percentage
• (b)25 Percentage
• (c)45 Percentage
• (d)55 Percentage

Answer

Correct Answer : (b) 25 Percentage
To find the rate of interest, we can use the formula for simple interest:
Simple Interest = (Principal × Rate × Time) / 100
Let’s assume the principal amount is P, and we know that it becomes three times in 8 years. So the amount after 8 years will be 3P.
We are given:
Principal (P)
Time (T) = 8 years
Amount (A) = 3P
We need to find the Rate (R).
Using the formula for simple interest, we have:
Simple Interest = A – P
Simple Interest = (P × R × T) / 100
A – P = (P × R × T) / 100
3P – P = (P × R × 8) / 100
2P = (P × R × 8) / 100
200P = P × R × 8
200 = R × 8
R = 200 / 8
R = 25
Therefore, the rate of interest is 25%.

(13) Mr. Johnson lends Rs. 6000 at 5% p.a. and Rs. 8000 at 6% p.a. What is the total interest at the end of one year?

• (a)780 Rupees
• (b)850 Rupees
• (c)750 Rupees
• (d)950 Rupees

Answer

Correct Answer : (a) 780 Rupees
To calculate the total interest at the end of one year, we need to find the interest earned on each amount separately and then add them together.
For Rs. 6000 at 5% p.a., the interest earned can be calculated as:
Interest_1 = (Principal_1 * Rate_1 * Time) / 100
Interest_1 = (6000 * 5 * 1) / 100
Interest_1 = Rs. 300
For Rs. 8000 at 6% p.a., the interest earned can be calculated as:
Interest_2 = (Principal_2 * Rate_2 * Time) / 100
Interest_2 = (8000 * 6 * 1) / 100
Interest_2 = Rs. 480
The total interest earned at the end of one year is the sum of the interest earned on each amount:
Total_interest = Interest_1 + Interest_2
Total_interest = Rs. 300 + Rs. 480
Total_interest = Rs. 780
Therefore, the total interest earned at the end of one year when Mr. Johnson lends Rs. 6000 at 5% p.a. and Rs. 8000 at 6% p.a. is Rs. 780.

(14) If the interest on Rs. 800 for 5 years is Rs. 120, find the rate of interest.

• (a)2 Percentage
• (b)3 Percentage
• (c)5 Percentage
• (d)4 Percentage

Answer

Correct Answer : (b) 3 Percentage
To find the rate of interest, we can use the formula for simple interest:
Rate of interest = (Interest * 100) / (Principal * Time)
Given:
Interest = Rs. 120
Principal = Rs. 800
Time = 5 years
Substituting the given values into the formula, we have:
Rate of interest = (120 * 100) / (800 * 5)
Calculating the expression:
Rate of interest = 12000 / 4000
Rate of interest = 3
Therefore, the rate of interest is 3%.

(15) The difference between simple interest and compound interest on an amount of Rs. 15000 for 2 years at 8% per annum is?

• (a)90 Rupees
• (b)80 Rupees
• (c)96 Rupees
• (d)70 Rupees

Answer

Correct Answer : (c) 96 Rupees
To calculate the difference between simple interest and compound interest on an amount of Rs. 15000 for 2 years at 8% per annum, we can use the formulas for simple interest and compound interest.
Let’s start with simple interest:
Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = (15000 × 8 × 2) / 100
Simple Interest = Rs. 2400
Now, let’s calculate the compound interest using the formula:
Compound Interest = Principal × (1 + Rate/100)^Time – Principal
Compound Interest = 15000 × (1 + 8/100)^2 – 15000
Compound Interest = 15000 × (1.08)^2 – 15000
Compound Interest = 15000 × 1.1664 – 15000
Compound Interest = Rs. 2496
The difference between the compound interest and simple interest is:
Difference = Compound Interest – Simple Interest
Difference = 2496 – 2400
Difference = Rs. 96
Therefore, the difference between the simple interest and compound interest on an amount of Rs. 15000 for 2 years at 8% per annum is Rs. 96.