Question

a man sells an article at 5% above its cost price if he had bought it at 5% less than what he had paid for it and sold it at 2 Rupees less he would have gained 10% find the cost price of the article

Answer 1

Let the cost price of the article = Rs x
He sold the article 5% above the cost price
So, sold price of the article = x + 5% of x
                                              = x + 5/100 * x
                                              = x + x/20
                                              = Rs 21x/20

He had bought the article 5% below the cost price. 
So, cost price for him =  x - 5% of x
                                     = x - 5/100*x
                                     = x - x/20
                                     = Rs 19x/20

He sold the article Rs 2 less
So, now sold price = Rs 21x/20 - 2
                                = Rs (21x - 40)/2

Profit on the article = (21x - 40)/20 - 19x/20
                                 =  (21x - 19x - 40)/20
                                 = (2x - 40)/20

Profit% = profit/C.P * 100
10 = (2x - 40)/20 * 20/19x * 100
10 = (2x - 40)/19x *100
1/10 = (2x - 40)/19x
19x = 20x - 400
x = Rs 400

The cost price of the article is Rs 400.

Hope this helps you.

Answer 2

let cost price be x rs

therefore selling price is , x + 5x/100

= x + x/20
= 21x/20

now if the cost price was , x - 5x/100 that is 19x /20 rs

and selling price was 21x/20 -2


then , profit will 10 %


so we can write ,

19x /20 + (19x /20) ×10/100 = 21x/20 -2

19x /20 + 19x /200 = 21x-40 /20

209x / 200 = 210x -400 / 200


209 x = 210 x - 400

x = 400 rs

therefore cost price is 400 rs