Aptitude : True Discounts

(6) A man purchased a bike for Rs. 5000 and sold it the same day for Rs. 6000, allowing the buyer a credit of 4 years. If the rate of interest be 14% per annum, then the man has a gain of

• (a)350 Rs
• (b)384 Rs
• (c)395 Rs
• (d)385 Rs

Answer

Correct Answer : (b) 384 Rs
The man has a gain of Rs. 6000 – Rs. 5000 = Rs. 1000.
The interest on Rs. 1000 for 4 years at 14% is 1000 * 14/100 * 4 = Rs. 616.
Therefore, the man’s net gain is Rs. 1000 – Rs. 616 = Rs. 384.
So the answer is 384

(7) A trader owes a supplier Rs. 20,042 due 3 years hence. The trader wants to settle the account after 6 months. If the rate of interest 18% per annum, how much cash should he pay?

• (a)17481 Rs
• (b)18500 Rs
• (c)14500 Rs
• (d)13525 Rs

Answer

Correct Answer : (a) 17481 Rs
Amount owed to the supplier (Future Value): Rs. 20,042
Time until the debt is due: 3 years
Rate of interest: 18% per annum
Time until the trader wants to settle the account: 6 months
First, let’s convert the rate of interest to a semi-annual rate since the trader wants to settle the account after 6 months. Divide the annual interest rate by 2:
Semi-annual interest rate = 18% / 2 = 9% per 6 months
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. 20,042, the interest rate is 9% (per 6 months), and the number of periods is 1.5 (3 years / 6 months).
Present Value = 20,042 / (1 + 0.09)^1.5
Calculating the present value:
Present Value = 20,042 / (1.09)^1.5
Present Value = 20,042 / 1.14641
Present Value ? 17481
Therefore, the trader should pay approximately Rs. 17,481.35 in cash to settle the account after 6 months.

(8) A woman wants to sell her laptop. There are two offers, one at Rs. 32,000 cash and the other a credit of Rs. 36,880 to be paid after 12 months, money being at 22% per annum. Which is the better offer?

• (a)35500 Rs
• (b)32000 Rs
• (c)36000 Rs
• (d)33000 Rs

Answer

Correct Answer : (b) 32000 Rs
Cash offer: Rs. 32,000
Credit offer: Rs. 36,880 to be paid after 12 months
Interest rate: 22% 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. 36,880
r is the interest rate per period (per annum rate divided by the number of periods)
n is the number of periods (12 months)
Let’s calculate the present value of the credit offer:
Present Value = 36,880 / (1 + 0.22)^1
Present Value = 36,880 / 1.22
Present Value ? 30,229.51
The present value of the credit offer is approximately Rs. 30,229.51.
Now, let’s compare the present value of the cash offer (Rs. 32,000) with the present value of the credit offer (Rs. 30,229.51). The higher present value represents the better offer.
In this case, the cash offer of Rs. 32,000 is higher than the present value of the credit offer (Rs. 30,229.51). Therefore, the better offer is the cash offer of Rs. 32,000.

(9) If Rs. 20 be allowed as true discount on a bill of Rs. 220 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)44 Rs
• (b)35 Rs
• (c)28 Rs
• (d)40 Rs

Answer

Correct Answer : (d) 40 Rs
Present Value = Face Value / (1 + Interest Rate)^Time
= 220 / (1 + 0.02)^Time
= 200
Simple Interest = Principal * Interest Rate * Time
= 200 * 0.02 * 2
= Rs. 40

(10) A man buys a mobile for Rs. 3950 in cash and sells it for Rs. 4200 at a credit of 3 years. If the rate of interest is 14% per annum, the man can make a profit of ____.

• (a)250 Rs
• (b)175 Rs
• (c)195 Rs
• (d)275 Rs

Answer

Correct Answer : (a) 250 Rs
Cost Price = Rs. 3950
Selling Price = Rs. 4200
Profit = Selling Price – Cost Price = 4200 – 3950 = Rs. 250
The man makes a profit of Rs. 250. However, he has to wait for 3 years to get the full amount. If he had sold the mobile for cash, he would have got Rs. 3950 immediately.
So, the man has to weigh the pros and cons of selling the mobile on credit. If he needs the money immediately, he should sell it for cash. However, if he can wait for 3 years, he can make a profit of Rs. 250