By selling an article for Rs.x, there is a loss of 15%. By selling the same article for Rs.y, there is a profit of 15%. What is the ratio of (y-x) and (y+x)?

sol. Let the cost price of the article be C.

When the article is sold for Rs. x, there is a loss of 15%. Therefore, the selling price is:

x = C - 0.15C = 0.85C

Similarly, when the article is sold for Rs. y, there is a profit of 15%. Therefore, the selling price is:

y = C + 0.15C = 1.15C

We need to find the ratio of (y-x) and (y+x):

(y-x) / (y+x) = [(1.15C - 0.85C) / (1.15C + 0.85C)]

= 0.3C / 2C

= 0.15

Therefore, the required ratio is 0.15:1 or simply 3:20.

2nd:-

If the cost price of the article is C = 100, then:

• Selling price when sold for x with a loss of 15%: x = C - 0.15C = 0.85C = 0.85 x 100 = 85 So, x = 85
• Selling price when sold for y with a profit of 15%: y = C + 0.15C = 1.15C = 1.15 x 100 = 115 So, y = 115

Therefore, when the cost price is 100, the selling prices are x = 85 and y = 115.

we can calculate the ratio of (y-x)/(x+y):

(y-x)/(x+y) = (115-85)/(85+115) = 30/200 = 0.15

So, the required ratio is 0.15 or simply 3:20.