Aptitude : True Discounts

(11) A woman purchased a farm for Rs. 6000 and sold it the same day for Rs. 7200, allowing the buyer a credit of 5 years. If the rate of interest be 16% per annum, then the woman has a gain of

• (a)6500 Rs
• (b)6960 Rs
• (c)6250 Rs
• (d)7100 Rs

Answer

Correct Answer : (b) 6960 Rs
Purchase price: Rs. 6000
Selling price: Rs. 7200
Time: 5 years
Interest rate: 16% per annum
First, let’s calculate the interest earned by the woman 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 = 7200 * 0.16 * 5
Interest = 5760
The interest earned by the woman on the credit provided is Rs. 5760.
Now, let’s calculate the gain made by the woman:
Gain = Selling Price – Purchase Price + Interest Earned
Gain = 7200 – 6000 + 5760
Gain = 6960
Therefore, the woman has a gain of Rs. 6960

(12) A retailer owes a wholesaler Rs. 25,049 due 4 years hence. The retailer wants to settle the account after 8 months. If the rate of interest 20% per annum, how much cash should he pay?

• (a)22500 Rs
• (b)22000 Rs
• (c)22117 Rs
• (d)26500 Rs

Answer

Correct Answer : (c) 22117 Rs
Amount owed to the wholesaler (Future Value): Rs. 25,049
Time until the debt is due: 4 years
Rate of interest: 20% per annum
Time until the retailer wants to settle the account: 8 months
First, let’s convert the rate of interest to a monthly rate since the retailer wants to settle the account after 8 months. Divide the annual interest rate by 12:
Monthly interest rate = 20% / 12 = 1.67% 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. 25,049, the interest rate is 1.67% (per month), and the number of periods is 8/12 (8 months / 12 months per year).
Present Value = 25,049 / (1 + 0.0167)^(8/12)
Calculating the present value:
Present Value = 25,049 / (1.0167)^(8/12)
Present Value = 25,049 / 1.13248
Present Value ? 22117
Therefore, the retailer should pay approximately Rs. 22117 in cash to settle the account after 8 months.

(13) A man wants to sell his boat. There are two offers, one at Rs. 42,000 cash and the other a credit of Rs. 48,880 to be paid after 14 months, money being at 24% per annum. Which is the better offer?

• (a)42000 Rs
• (b)48880 Rs
• (c)0 Rs
• (d)0 Rs

Answer

Correct Answer : (a) 42000 Rs
To determine the better offer, we need to compare the present value of the cash offer and the present value of the credit offer. The present value will help us evaluate the current worth of the future payment at a given interest rate.
Given information:
Cash offer: Rs. 42,000
Credit offer: Rs. 48,880 to be paid after 14 months
Interest rate: 24% 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. 48,880
r is the interest rate per period (per annum rate divided by the number of periods)
n is the number of periods (14 months)
Let’s calculate the present value of the credit offer:
Present Value = 48,880 / (1 + 0.24)^(14/12)
Present Value ? 40,870.63
The present value of the credit offer is approximately Rs. 40,870.63.
Now, let’s compare the present value of the cash offer (Rs. 42,000) with the present value of the credit offer (Rs. 40,870.63). The higher present value represents the better offer.
In this case, the cash offer of Rs. 42,000 is higher than the present value of the credit offer (Rs. 40,870.63). Therefore, the better offer is the cash offer of Rs. 42,000.

(14) If Rs. 25 be allowed as true discount on a bill of Rs. 275 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)225 Rs
• (b)0 Rs
• (c)125 Rs
• (d)150 Rs

Answer

Correct Answer : (b) 0 Rs
True discount is the difference between the face value (amount due) and the present value (amount to be paid) of a bill.
Given information:
Original bill amount: Rs. 275
True discount allowed: Rs. 25
Let’s calculate the present value of the original bill using the formula for true discount:
Present Value = Face Value – True Discount
Present Value = 275 – 25
Present Value = 250
So, the present value of the original bill is Rs. 250.
Now, we need to find the discount allowed on the same sum due at the end of double the time. If the time is doubled, the period is increased by a factor of 2.
Let’s calculate the discount allowed on the same sum due at the end of double the time:
Discount = Face Value – Present Value
Discount = 275 – 2 * Present Value
Discount = 275 – 2 * 250
Discount = 275 – 500
Discount = -225
The discount allowed on the same sum due at the end of double the time is Rs. -225. However, since a discount cannot be negative, we can interpret this result as no discount being allowed or a premium of Rs. 225 being charged at the end of double the time.

(15) A woman buys a laptop for Rs. 4950 in cash and sells it for Rs. 5200 at a credit of 4 years. If the rate of interest is 16% per annum, the woman earned is :

• (a)3500 Rs
• (b)4100 Rs
• (c)2500 Rs
• (d)3168 Rs

Answer

Correct Answer : (d) 3168 Rs
Purchase price: Rs. 4950 (bought in cash)
Selling price: Rs. 5200 (sold on credit)
Time: 4 years
Interest rate: 16% per annum
First, let’s calculate the interest earned by the woman when selling the laptop on credit. We’ll use the simple interest formula:
Interest = Principal * Rate * Time
Where:
Principal is the purchase price
Rate is the interest rate per annum
Time is the number of years
Interest = 4950 * 0.16 * 4
Interest = 3168
The interest earned by the woman when selling the laptop on credit is Rs. 3168