Aptitude : Simple Interest

(21) A sum of Rs. 8000 is lent out in two parts. One part is lent at 5% per annum and the other is lent at 2% per annum. The total interest at the end of one year is Rs. 350. Find the sum lent at each rate.

• (a)Rs5000 at 5 percentage and Rs3000 at 2 percentage
• (b)Rs4000 at 5 percentage and Rs3000 at 2 percentage
• (c)Rs5000 at 5 percentage and Rs4000 at 2 percentage
• (d)Rs5000 at 6 percentage and Rs3000 at 2 percentage

Answer

Correct Answer : (a) Rs5000 at 5 percentage and Rs3000 at 2 percentage
principal_amount_1 = 5000
principal_amount_2 = 3000
interest_rate_1 = 5
interest_rate_2 = 2
time_period = 1
Let x be the sum lent at 5% and y be the sum lent at 2%.
We know that x + y = 8000 and 0.05x + 0.02y = 350.
Solving for x and y, we get x = 5000 and y = 3000.
Therefore, the sum lent at 5% is Rs. 5000 and the sum lent at 2% is Rs. 3000.

(22) A sum of Rs. 10000 yields a simple interest of Rs. 7000 in 7 years. What is the rate of interest?

• (a)10 Percentage
• (b)15 Percentage
• (c)19 Percentage
• (d)9 Percentage

Answer

Correct Answer : (a) 10 Percentage
The simple interest formula is:
Simple Interest = (Principal * Rate * Time) / 100
We are given:
Principal = Rs. 10000
Simple Interest = Rs. 7000
Time = 7 years
Plugging in the given values into the formula, we can calculate the rate:
7000 = (10000 * Rate * 7) / 100
7000 * 100 = 10000 * Rate * 7
700000 = 70000 * Rate
Dividing both sides by 70000 to solve for Rate:
Rate = 700000 / 70000
Rate = 10
Therefore, the rate of interest is 10%.

(23) If the simple interest on Rs. 2000 is Rs. 300 at the end of 3 years, what is the rate of interest?

• (a)7 Percentage
• (b)5 Percentage
• (c)8 Percentage
• (d)9 Percentage

Answer

Correct Answer : (b) 5 Percentage
The simple interest formula is:
Simple Interest = (Principal * Rate * Time) / 100
We are given:
Principal = Rs. 2000
Simple Interest = Rs. 300
Time = 3 years
Plugging in the given values into the formula, we can calculate the rate:
300 = (2000 * Rate * 3) / 100
300 * 100 = 2000 * Rate * 3
30000 = 6000 * Rate
Dividing both sides by 6000 to solve for Rate:
Rate = 30000 / 6000
Rate = 5
Therefore, the rate of interest is 5%.

(24) A sum of Rs. 5000 is borrowed at a simple interest of 6% per annum. What is the amount after 3 years?

• (a)5900 Rupees
• (b)5000 Rupees
• (c)4500 Rupees
• (d)5250 Rupees

Answer

Correct Answer : (a) 5900 Rupees
The formula to calculate the amount with simple interest is:
Amount = Principal + (Principal * Rate * Time) / 100
We are given:
Principal = Rs. 5000
Rate = 6% per annum
Time = 3 years
Plugging in the given values into the formula, we can calculate the amount:
Amount = 5000 + (5000 * 6 * 3) / 100
Amount = 5000 + 900
Amount = Rs. 5900
Therefore, the amount after 3 years will be Rs. 5900.

(25) If Rs. 1200 is divided into two parts such that the interest on one part at 12% for 2 years is equal to the interest on the other part at 6% for 3 years, what are the two parts?

• (a)Rs:400,Rs:800
• (b)Rs:400,Rs:900
• (c)Rs:500,Rs:800
• (d)Rs:600,Rs:800

Answer

Correct Answer : (a) Rs:400,Rs:800
Let’s assume one part of Rs. 1200 is invested at 12% for 2 years, and the other part is invested at 6% for 3 years.
Let the amount invested at 12% be x, and the amount invested at 6% be (1200 – x) (since the total amount is Rs. 1200).
The interest earned on the amount invested at 12% is (x * 12% = 0.12x),
and the interest earned on the amount invested at 6% is ((1200 – x) * 6% = 0.06(1200 – x)).
According to the given information, both interests are equal, so we can set up the equation:
0.12x = 0.06(1200 – x)
Simplifying the equation:
0.12x = 0.06 * 1200 – 0.06x
0.12x = 72 – 0.06x
0.12x + 0.06x = 72
0.18x = 72
x = 72 / 0.18
x = 400
Therefore, one part of Rs. 1200 is Rs. 400, and the other part is (1200 – 400) = Rs. 800.