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Two articles are sold for the same price such that a profit of 15% is made on one and a loss of 15% is made on the other. Find the gain or the loss per cent on the whole.

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2.25 % loss

2.25 % gain

5 % loss

5 % gain

answer is A.

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Detailed Solution

Suppose that.
The 1st cost of the article =

x

The 2nd cost of the article =

y

Profit in article
1st profit 15 % of its cost price

= \frac{15}{100} \times x

2nd loss 15 % of its cost price

= \frac{15}{100} \times y

Now using this method for
For 1st articles

selling price of first article = cost price + profit

= x + \frac{15}{100} \times x

For 2nd articles

selling price of second article = cost price - loss

= y - \frac{15}{100} \times y

As per given condition
Selling price of both article are equal. So,

x + \frac{15}{100} \times x = y - \frac{15}{100} \times y

Solving for x in terms of y then

\frac{100 + 15}{100} \times x = \frac{100 - 15}{100} \times y

\Rightarrow x = \frac{85}{115} \times y

……… (1)
Now calculate the profit

\frac{profit in article one - loss in the second article}{total selling price of both article} \times 100

= \frac{\frac{15 x}{100} - \frac{15 y}{100}}{x + y} \times 100

= \frac{15 (x - y)}{x + y}

Put the value of x in equation (1) we obtain

= \frac{15 (\frac{85}{115} -)}{\frac{85}{115} +}

= \frac{15 (85 - 115)}{85 + 115} [we take 115 LCM from both numerator and denomator]

= \frac{15 (85 - 115)}{85 + 115}

= - \frac{15 \times 3}{20}

= - \frac{3 \times 3}{4}

= - \frac{9}{4}

= - 2.25

Negative sign suggest that there is loss.
Therefore, the two articles as a whole are sold for a loss of 2.25%.
Option 1 is correct.

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