Question

A shopkeepers marked price of an article is 140% of the cost price. He sold the articles under two schemes. Scheme 1 is to sell each article at a discount of 10% and scheme 2 to sell two articles at a discount of 15% each. He sold 60% of the articles under scheme 2 and the remaining under scheme 1. What is his overall gain or loss percentage?

• A. 0.08%loss
• B. 11.8%gain
• C. 13.6%gain
• D. 21.8%gain
• E. 23.6%gain

Answer 1

The Correct Option is D

The correct answer is option (D):

21.8%gain

Let's break down this problem step by step to understand how to arrive at the correct answer.

First, let's assign variables:

* Let the cost price (CP) of a single article be 'x'.
* The marked price (MP) is 140% of the cost price, so MP = 1.40x.

Now, let's analyze the two schemes:

Scheme 1:

* Discount = 10%
* Selling Price (SP) = MP - Discount = 1.40x - 0.10(1.40x) = 1.40x - 0.14x = 1.26x

Scheme 2:

* Discount = 15% on each article (when buying two)
* For two articles:
* Total MP = 2 * 1.40x = 2.80x
* Discount = 15% of 2.80x = 0.15 * 2.80x = 0.42x
* SP for two articles = 2.80x - 0.42x = 2.38x
* SP for one article = 2.38x / 2 = 1.19x

Now, let's consider the proportions of articles sold under each scheme:

* 60% of articles sold under Scheme 2
* 40% of articles sold under Scheme 1

Let's assume the shopkeeper had 100 articles.

* Articles sold under Scheme 2: 60 articles
* Articles sold under Scheme 1: 40 articles

Calculate the total revenue from each scheme:

* Scheme 2: 60 articles sold in pairs (30 pairs), therefore revenue = 30 * 2.38x = 71.4x
* Scheme 1: 40 articles sold, therefore revenue = 40 * 1.26x = 50.4x

Calculate total revenue:

* Total Revenue = 71.4x + 50.4x = 121.8x

Calculate the total cost price:

* Total CP = 100 * x = 100x

Calculate the overall profit:

* Profit = Total Revenue - Total CP = 121.8x - 100x = 21.8x

Calculate the profit percentage:

* Profit Percentage = (Profit / Total CP) * 100
* Profit Percentage = (21.8x / 100x) * 100 = 21.8%

Therefore, the overall gain is 21.8%.