Aptitude : True Discounts

(16) A man purchased a house for Rs. 7000 and sold it the same day for Rs. 8400, allowing the buyer a credit of 6 years. If the rate of interest be 18% per annum, then the man has a gain of

• (a)12500 Rs
• (b)11500 Rs
• (c)10472 Rs
• (d)9500 Rs

Answer

Correct Answer : (c) 10472 Rs
Purchase price: Rs. 7000
Selling price: Rs. 8400
Time: 6 years
Interest rate: 18% per annum
First, let’s calculate the interest earned by the man on the credit provided to the buyer. We’ll use the simple interest formula:
Interest = Principal * Rate * Time
Where:
Principal is the selling price
Rate is the interest rate per annum
Time is the number of years
Interest = 8400 * 0.18 * 6
Interest = 9072
The interest earned by the man on the credit provided is Rs. 9072.
Now, let’s calculate the gain made by the man:
Gain = Selling Price – Purchase Price + Interest Earned
Gain = 8400 – 7000 + 9072
Gain = 10472
Therefore, the man has a gain of Rs. 10472

(17) A trader owes a supplier Rs. 30,056 due 5 years hence. The trader wants to settle the account after 10 months. If the rate of interest 22% per annum, how much cash should he pay?

• (a)25000 Rs
• (b)24964 Rs
• (c)23000 Rs
• (d)22500 Rs

Answer

Correct Answer : (b) 24964 Rs
Amount owed to the supplier (Future Value): Rs. 30,056
Time until the debt is due: 5 years
Rate of interest: 22% per annum
Time until the trader wants to settle the account: 10 months
First, let’s convert the rate of interest to a monthly rate since the trader wants to settle the account after 10 months. Divide the annual interest rate by 12:
Monthly interest rate = 22% / 12 = 1.83% per month
Next, let’s calculate the present value of the debt using the formula for the present value of a single sum:
Present Value = Future Value / (1 + r)^n
Where:
r is the interest rate per period
n is the number of periods
In this case, the future value is Rs. 30,056, the interest rate is 1.83% (per month), and the number of periods is 10/12 (10 months / 12 months per year).
Present Value = 30,056 / (1 + 0.0183)^(10/12)
Calculating the present value:
Present Value = 30,056 / (1.0183)^(10/12)
Present Value = 30,056 / 1.202154
Present Value ? 24,964.70
Therefore, the trader should pay approximately Rs. 24964 in cash to settle the account after 10 months.

(18) A woman wants to sell her furniture. There are two offers, one at Rs. 52,000 cash and the other a credit of Rs. 60,880 to be paid after 16 months, money being at 26% per annum. Which is the better offer?

• (a)52000 Rs
• (b)60880 Rs
• (c)0 Rs
• (d)0 Rs

Answer

Correct Answer : (a) 52000 Rs
Cash offer: Rs. 52,000
Credit offer: Rs. 60,880 to be paid after 16 months
Interest rate: 26% per annum
Let’s calculate the present value of the credit offer first. We’ll use the formula for the present value of a single sum:
Present Value = Future Value / (1 + r)^n
Where:
Future Value is Rs. 60,880
r is the interest rate per period (per annum rate divided by the number of periods)
n is the number of periods (16 months)
Let’s calculate the present value of the credit offer:
Present Value = 60,880 / (1 + 0.26)^(16/12)
Present Value ? 49,566.51
The present value of the credit offer is approximately Rs. 49,566.51.
Now, let’s compare the present value of the cash offer (Rs. 52,000) with the present value of the credit offer (Rs. 49,566.51). The higher present value represents the better offer.
In this case, the cash offer of Rs. 52,000 is higher than the present value of the credit offer (Rs. 49,566.51). Therefore, the better offer is the cash offer of Rs. 52,000

(19) If Rs. 30 be allowed as true discount on a bill of Rs. 330 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is

• (a)37500 Rs
• (b)36556 Rs
• (c)35566 Rs
• (d)32566 Rs

Answer

Correct Answer : (c) 35566 Rs
Principal = Rs. 30,056
Interest rate = 22%
Time = 10/12 years = 0.83 years
Simple Interest = Principal * Interest Rate * Time
= 30056 * 22/100 * 0.83
= Rs. 5,682.15
Amount = Principal + Interest
= 30056 + 5682.15
= Rs. 35,566.27
The trader has to pay the interest for 10 months, which is 0.83 years. The simple interest for this period is Rs. 5,682.15. The trader has to pay the principal amount of Rs. 30,056 plus the interest amount of Rs. 5,682.15, for a total of Rs. 35566

(20) A man buys a car for Rs. 5950 in cash and sells it for Rs. 6200 at a credit of 5 years. If the rate of interest is 18% per annum, the man makes a loss of

• (a)100 Rupees
• (b)25 Rupees
• (c)75 Rupees
• (d)95 Rupees

Answer

Correct Answer : (c) 75 Rupees
The man makes a loss of Rs. 75.
Here’s the calculation:
Cost Price = Rs. 5950
Selling Price = Rs. 6200
Simple Interest = (6200 – 5950) * 18/100 * 5 = Rs. 75
Net Loss = 6200 – (5950 + 75) = Rs. 75
The man has a net loss of Rs. 75 because he is not able to earn interest on the money he receives from the sale of the car.