Aptitude : Simple Interest

(16) Mr. Rodriguez invested Rs. 6000 for 1 year, part at 5% and the rest at 6%. His total interest is Rs. 350. How much did he invest at each rate?

• (a)Rs.1000 at 5% and Rs. 5000 at 6%
• (b)Rs.3000 at 5% and Rs. 5000 at 6%
• (c)Rs.2000 at 5% and Rs. 5000 at 6%
• (d)Rs.1000 at 5% and Rs. 6000 at 6%

Answer

Correct Answer : (a) Rs.1000 at 5% and Rs. 5000 at 6%
Let’s assume Mr. Rodriguez invested x amount of rupees at 5% interest rate and (6000 – x) amount of rupees at 6% interest rate.
The interest earned on the amount invested at 5% is calculated as (x * 5%) = 0.05x.
The interest earned on the amount invested at 6% is calculated as ((6000 – x) * 6%) = 0.06(6000 – x).
According to the given information, the total interest earned is Rs. 350, so we can set up the equation:
0.05x + 0.06(6000 – x) = 350
Simplifying the equation:
0.05x + 360 – 0.06x = 350
-0.01x = -10
x = -10 / -0.01
x = 1000
Therefore, Mr. Rodriguez invested Rs. 1000 at 5% interest rate and Rs. (6000 – 1000) = Rs. 5000 at 6% interest rate.

(17) A sum of money doubles itself at simple interest in 15 years. Find the rate of interest.

• (a)6.67 Percentage
• (b)8.05 Percentage
• (c)7.5 Percentage
• (d)6.05 Percentage

Answer

Correct Answer : (a) 6.67 Percentage
To find the rate of interest, we need to know the principal amount (the initial sum of money).
Let’s assume the principal amount is P.
According to the given information, the sum of money doubles itself in 15 years at simple interest. This means that after 15 years, the final amount is 2 times the principal amount.
Using the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
We can write the equation as:
P + (P * Rate * 15) / 100 = 2P
Simplifying the equation:
P + (15P * Rate) / 100 = 2P
Multiplying both sides by 100 to eliminate the denominator:
100P + 15P * Rate = 200P
Subtracting 100P from both sides:
15P * Rate = 100P
Dividing both sides by 15P:
Rate = 100P / (15P)
Rate = 100 / 15
Rate = 6.67
Therefore, the rate of interest is 6.67%.

(18) How much money should be invested at 10% simple interest in order to earn Rs. 200 in 2 years?

• (a)750 Rupees
• (b)1000 Rupees
• (c)1500 Rupees
• (d)1250 Rupees

Answer

Correct Answer : (b) 1000 Rupees
To find the amount of money that should be invested at 10% simple interest to earn Rs. 200 in 2 years, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
We are given:
Simple Interest = Rs. 200
Rate = 10%
Time = 2 years
Let’s assume the principal amount is P.
Plugging in the given values into the formula, we can write the equation as:
200 = (P * 10 * 2) / 100
Simplifying the equation:
200 = (20P) / 100
Multiplying both sides by 100 to eliminate the denominator:
200 * 100 = 20P
20,000 = 20P
Dividing both sides by 20:
P = 20,000 / 20
P = 1,000
Therefore, Rs. 1,000 should be invested at 10% simple interest in order to earn Rs. 200 in 2 years.

(19) What sum of money will amount to Rs. 520 in 2 years at 4% per annum?

• (a)500 Rupees
• (b)520 Rupees
• (c)480 Rupees
• (d)540 Rupees

Answer

Correct Answer : (c) 480 Rupees
To find the principal amount that will amount to Rs. 520 in 2 years at 4% per annum, we can use the formula for compound interest:
Amount = Principal * (1 + Rate/100)^Time
We are given:
Amount = Rs. 520
Rate = 4%
Time = 2 years
Let’s assume the principal amount is P.
Plugging in the given values into the formula, we can write the equation as:
520 = P * (1 + 4/100)^2
Simplifying the equation:
520 = P * (1 + 0.04)^2
520 = P * (1.04)^2
520 = P * 1.0816
Dividing both sides by 1.0816 to solve for P:
P = 520 / 1.0816
P ? 480.23
Therefore, the sum of money that will amount to Rs. 520 in 2 years at 4% per annum is approximately Rs. 480.23.

(20) A sum of Rs. 15000 is borrowed at 5% per annum. What amount will be paid back at the end of 2 years?

• (a)17500 Rupees
• (b)18500 Rupees
• (c)17585 Rupees
• (d)16537 Rupees

Answer

Correct Answer : (d) 16537 Rupees
To calculate the amount that will be paid back at the end of 2 years for a sum of Rs. 15000 borrowed at 5% per annum, we need to consider compound interest.
The formula to calculate the amount with compound interest is:
Amount = Principal * (1 + Rate/100)^Time
We are given:
Principal (P) = Rs. 15000
Rate (R) = 5%
Time (T) = 2 years
Plugging in the given values into the formula, we can calculate the amount:
Amount = 15000 * (1 + 5/100)^2
Amount = 15000 * (1 + 0.05)^2
Amount = 15000 * 1.1025
Amount ? Rs. 16,537.50
Therefore, the amount that will be paid back at the end of 2 years for a sum of Rs. 15000 borrowed at 5% per annum is approximately Rs. 16,537.50.