Ajay sold an article at 20% profit to balu. balu sold it at 30% profit to chetan. dinesh sold a similar article at 20% loss to david. david sold it at 30% loss to edward. the sum of the price that chetan and edward paid for their respective article is rs 28000 more than what ajay paid. if ajay and dinesh bought the article for the same price find the sum of the prices paid by ajay and dinesh for their respective articles
How to do an easy way
Let's assume the cost price of the article for Ajay and Dinesh is "x" rupees.
Since Ajay sold the article at a 20% profit, he sold it for (100% + 20%) = 120% of the cost price:
So, Ajay sold the article for (120/100) * x = 1.2x rupees.
Balu bought the article from Ajay and sold it at a 30% profit. So, he sold it for (100% + 30%) = 130% of what he bought it for:
Balu paid 1.2x rupees for the article and sold it for (130/100) * 1.2x = 1.56x rupees.
Chetan paid 1.56x rupees for the article.
Similarly, Dinesh sold the article at a 20% loss. So, he sold it for (100% - 20%) = 80% of the cost price:
Dinesh sold the article for (80/100) * x = 0.8x rupees.
David bought the article from Dinesh and sold it at a 30% loss. So, he sold it for (100% - 30%) = 70% of what he bought it for:
David paid 0.8x rupees for the article and sold it for (70/100) * 0.8x = 0.56x rupees.
Edward paid 0.56x rupees for the article.
The sum of what Chetan and Edward paid is 1.56x + 0.56x = 2.12x.
Given that their sum is Rs 28000 more than what Ajay paid:
2.12x = 1.2x + 28000
Subtracting 1.2x from both sides:
0.92x = 28000
Dividing both sides by 0.92:
x = 28000 / 0.92 = 30434.78 (approx)
Therefore, the cost price of the article for Ajay and Dinesh is approximately Rs 30434.78.
The sum of the prices paid by Ajay and Dinesh for their respective articles is 2 * Rs 30434.78 = Rs 60869.56 (approx).
To find the sum of the prices paid by Ajay and Dinesh for their respective articles, we can solve the problem through a step-by-step approach:
1. Let's start by assuming the price at which Ajay bought the article as 'x'. As mentioned, the price at which Dinesh bought the similar article is the same, so Dinesh also bought the article for 'x' rupees.
2. Ajay sold the article at a 20% profit to Balu. To calculate the selling price to Balu, we need to add 20% of the cost price to the cost price. 20% of 'x' can be calculated as (20/100) * x = 0.2x. Therefore, Ajay sold the article to Balu for a price of x + 0.2x = 1.2x.
3. Balu then sold the article at a 30% profit to Chetan. Similarly, we need to add 30% of the cost price to the selling price to get the selling price to Chetan. 30% of 1.2x can be calculated as (30/100) * 1.2x = 0.36x. Therefore, Balu sold the article to Chetan for a price of 1.2x + 0.36x = 1.56x.
4. Dinesh sold a similar article at a 20% loss to David. To calculate the selling price to David, we need to subtract 20% of the cost price from the cost price. 20% of 'x' can be calculated as (20/100) * x = 0.2x. Therefore, Dinesh sold the article to David for a price of x - 0.2x = 0.8x.
5. David then sold the article at a 30% loss to Edward. Similarly, we need to subtract 30% of the cost price from the selling price to get the selling price to Edward. 30% of 0.8x can be calculated as (30/100) * 0.8x = 0.24x. Therefore, David sold the article to Edward for a price of 0.8x - 0.24x = 0.56x.
6. According to the given information, the sum of the prices paid by Chetan and Edward is Rs 28,000 more than what Ajay paid. So we can set up the equation as follows: 1.56x + 0.56x = x + 28,000.
7. Simplifying the equation, we get 2.12x = x + 28,000.
8. Subtracting x from both sides, we get 1.12x = 28,000.
9. Dividing both sides by 1.12, we get x = 25,000.
10. Therefore, Ajay and Dinesh both bought their respective articles for Rs 25,000 each.
11. The sum of the prices paid by Ajay and Dinesh is 25,000 + 25,000 = Rs 50,000.
So, the sum of the prices paid by Ajay and Dinesh for their respective articles is Rs 50,000.
b = 1.20a
c = 1.30b
da = 0.80di
e = 0.70da
c+e = a+28000
a = di
Now just start substituting to find a+di