A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
Rs. 2160
Rs. 1420
Rs. 1580
Rs. 2210
Answers
The minimum profit that the merchant could have made on this trade is option (3): Rs. 1580.
Step-by-step explanation:
The C.P. of each article = Rs. 40
∴ The C.P. of 80 articles = 80 × 40 = Rs. 3200
It is given that the merchant sold n articles at n% profit and remaining at (100 - n)% profit, so we have
The profit from n objects = (n% * 40 )* n
And,
The profit from the remaining objects = [(100 – n)% × 40] × (80 – n)
Now, as it is asked in the question, we have to find the minimum possible value of
[(n% * 40 )* n] + [(100 – n)% * 40 * (80 – n)]
⇒ [n²] + [(8000 – 100n – 80n + n²)] ……. [removing % and 40 for easy calculation will not change the final required value]
⇒ n² + 8000 – 180n + n²
⇒ 2n² + 8000 – 180n
⇒ n² – 90n + 4000 …… [dividing by 2 throughout]
[Since the middle term is 90n so we will now add and subtract 2025 (a square of 45) in order to create an expression that can be expressed as a perfect square. This type of approach can be termed as the “Completion of Squares” approach]
⇒ n² – 90n + 4000 + 2025 – 2025
⇒ (n² – 90n + 2025) + (4000 - 2025)
⇒ (n – 45)² + 1975 ← This minimum expression is obtained when n = 45
Therefore, we can conclude that,
When n = 45, the minimum profit made by the merchant will be,
= [45% × 40 × 45] + [55% × 40 × (80-45)]
= [45 * 0.4 * 45] + [55 * 0.4 * 35]
= 810 + 770
= Rs. 1580
Thus, the minimum profit that the merchant could have made on this trade is Rs. 1580.
------------------------------------------------------------------------------------------------
Also View:
A retailers buy a TV from a wholesaler for 40000 rupees he marks the price of the TV 15% above his cost price and sells it to a consumer at 5% discount on the marked price if the sales are intra sales and the rate of GST is 12% (i) find the marked price of the TV (ii) the amount which consumer pays for the TV (iii) the amount of Tax (under GST) paid by the retailer to the central government (iii) the amount of Tax (under GST) received by the state government .
https://brainly.in/question/9599726
A wholesaler allows a discount of 20 % on the list price of an article to a retailer. The retailer sells it at a 5% discount on the list price . If the customer pays rs 38 for the article what is the retailer's profit ?
https://brainly.in/question/902358