SOLUTION: what was the cost price of an article which on being sold at a gain of 7.5% yields rupees 6 more if it was sold at a loss of 12.5%

Question 892109: what was the cost price of an article which on being sold at a gain of 7.5% yields rupees 6 more if it was sold at a loss of 12.5%
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the cost of the article.

the sale price with a gain of 7.5% is equal to 1.075*x

the sale price with a loss of 12.5% is equal to .875*x

your equation is 1.075*x = .875*x + 6

this means that the sale price with a gain of 7.5% is 6 more than the sale price with a loss of 12.5%.

solve for x in this equation and you will get x = 30.

when x = 30, you get:

1.075 * 30 = 32.25

.875 * 30 = 26.25

add 6 to 26.25 and you get 32.25

1.075 * x was derived as follows:

x + .075 * x = (1 + .075) * x = 1.075 * x

.875 * x was derived as follows:

x - .125 * x = (1 - .125) * x = .875 * x

the equation of 1.075 * x = .875 * x + 6 was solved as follows:

subtract .875 * x from both sides of the equation to get:

1.075 * x - .875 * x = 6

factor out the x to get:

(1.075 - .875) * x = 6

simplify to get:

.2 * x = 6

divide both sides of this equation to get x = 6 / .2

solve for x to get x = 30.

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