Question

A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the best offer?
(A) Rs. 12,000 in cash
(B) Rs. 12,880 at credit
(C) Both are equally good.
(D) None of these

Answer 1

Hint: Here, we have two cases. In the \[{{1}^{st}}\] case, the scooter is being sold at Rs. 12,000 cash. So, the present worth of the scooter is equal to Rs. 12,000. In the \[{{2}^{nd}}\] case, it is given that the scooter is being sold at a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Convert the time 8 months into year using the relation, \[\text{12}\,\text{months=1}\,\text{year}\] . Now, calculate the present worth using the formula, \[\text{Present}\,\text{worth=}\dfrac{\text{100 }\!\!\times\!\!\text{ Amount}}{\left( \text{100+rate }\!\!\times\!\!\text{ time} \right)}\] . Now, compare the present worth in both cases and figure out which is the best offer.

Complete step by step solution:
According to the question, we have two cases.
In the \[{{1}^{st}}\] case, it is given that the scooter is being sold at Rs. 12,000 cash.
The present worth of the scooter = Rs. 12,000 ……………………………….(1)
In the \[{{2}^{nd}}\] case, it is given that the scooter is being sold at a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum.
The rate at which the amount would be paid = 18% …………………………(2)
The time taken to clear the amount = 8 months …………………………………..(3)
The amount to be paid after 8 months = Rs. 12,880 ……………………………….(4)
We know that there are 12 months in a year.
\[\Rightarrow \text{12}\,\text{months=1}\,\text{year}\]
\[\Rightarrow \text{1}\,\text{month=}\dfrac{\text{1}}{\text{12}}\text{ year}\] …………………………………….(5)
Now, from equation (3) and equation (5), we get
The time taken to clear the amount = \[\dfrac{8}{12}\] year = \[\dfrac{2}{3}\] year …………………………..(6)
We know the formula, \[\text{Present}\,\text{worth=}\dfrac{\text{100 }\!\!\times\!\!\text{ Amount}}{\left( \text{100+rate }\!\!\times\!\!\text{ time} \right)}\] …………………………………(7)
Now, from equation (2), equation (4), and equation (7), we get
The present worth of the credit = Rs. \[\dfrac{\text{100 }\!\!\times\!\!\text{ 12880}}{\left( \text{100+18 }\!\!\times\!\!\text{ }\dfrac{2}{3} \right)}\] = Rs. \[\dfrac{1288000}{\left( 100+12 \right)}\] = Rs. \[\dfrac{1288000}{112}\] = Rs. 11,500.
At present the worth of the credit amount is Rs. 11,500 ………………………….(8)
From equation (1) and equation (8), we have the present worth of the scooter in the first case and the second case respectively.
We can say that the present worth is more in the second case.
Therefore, surely cash of Rs. 12,000 is the best offer.
Hence, option (A) is the correct one.

Note: Since Rs. 12,880 is more than Rs. 12,000 so, one might go with the option (B). This is wrong because of an amount Rs. 12,880 is getting paid after 8 months. So, first, we have to figure out the present worth of that amount. After calculating the present worth, we can figure out which is the best offer.