Aptitude : True Discounts

(21) A woman purchased a shop for Rs. 8000 and sold it the same day for Rs. 9600, allowing the buyer a credit of 7 years. If the rate of interest be 20% per annum, then the woman has a gain of:

• (a)2400 Rupees
• (b)1600 Rupees
• (c)1200 Rupees
• (d)1750 Rupees

Answer

Correct Answer : (b) 1600 Rupees
Cost Price = Rs. 8000
Selling Price = Rs. 9600
Simple Interest = (9600 – 8000) * 20/100 * 7 = Rs. 1600
Net Gain = 9600 – (8000 + 1600) = Rs. 1600
The woman has a net gain of Rs. 1600 because she is able to earn interest on the money she receives from the sale of the shop.

(22) A retailer owes a wholesaler Rs. 35,063 due 6 years hence. The retailer wants to settle the account after 12 months. If the rate of interest 24% per annum, how much cash should he pay?

• (a)30500 Rupees
• (b)31250 Rupees
• (c)31366 Rupees
• (d)3250 Rupees

Answer

Correct Answer : (c) 31366 Rupees
Amount owed: Rs. 35,063
Time remaining: 6 years
Rate of interest: 24% per annum
To calculate the present value, we can use the formula:
Present Value = Future Value / (1 + Rate)^Time
First, let’s calculate the future value of the amount owed after 6 years:
Future Value = Amount owed = Rs. 35,063
Next, let’s calculate the present value after 12 months (1 year):
Present Value = Future Value / (1 + Rate)^Time
= Rs. 35,063 / (1 + 0.24)^6/12
= Rs. 35,063 / (1.24)^(1/2)
? Rs. 31,366.79
Therefore, the retailer should pay approximately Rs. 31366 in cash to settle the account after 12 months.

(23) A man wants to sell his TV. There are two offers, one at Rs. 62,000 cash and the other a credit of Rs. 72,880 to be paid after 18 months, money being at 28% per annum. Which is the better offer?

• (a)72880 Rupees
• (b)62000 Rupees
• (c)0 Rupees
• (d)0 Rupees

Answer

Correct Answer : (b) 62000 Rupees
Cash offer: Rs. 62,000
Credit offer: Rs. 72,880 to be paid after 18 months
Rate of interest: 28% per annum
To calculate the present value of the credit offer, we can use the formula:
Present Value = Future Value / (1 + Rate)^Time
First, let’s calculate the present value of the credit offer after 18 months:
Present Value = Rs. 72,880 / (1 + 0.28)^(18/12)
? Rs. 61,570.59
Comparing the present value of the credit offer (Rs. 61,570.59) with the cash offer (Rs. 62,000), we find that the cash offer is higher.
Therefore, the better offer is the cash offer of Rs. 62000.

(24) If Rs. 35 be allowed as true discount on a bill of Rs. 385 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)40 Rupees
• (b)55 Rupees
• (c)35 Rupees
• (d)25 Rupees

Answer

Correct Answer : (c) 35 Rupees
Let’s break down the given information:
Bill amount: Rs. 385
True discount: Rs. 35
To find the original rate of discount, we can use the formula:
Original Rate of Discount = (Discount / Bill Amount) * 100
Substituting the given values, we have:
Original Rate of Discount = (35 / 385) * 100 = 9.09%
Now, we need to calculate the discount for double the time. Since the original discount rate remains the same, we can use the formula:
Discount = (Original Rate of Discount / 100) * Bill Amount
Substituting the values, we get:
Discount = (9.09 / 100) * 385 = Rs. 35
Therefore, the discount allowed on the same sum due at the end of double the time is also Rs. 35