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.

2.25 %

loss

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2.25 %

gain

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5 %

loss

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5 %

gain

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Solution

The correct option is A $2.25 %$ loss

For the first article,
Given, profit $% = 15 %$

Profit $% = \frac{S P - C P_{1}}{C P_{1}} \times 100 = 15 %$
$\Rightarrow \frac{S P - C P_{1}}{C P_{1}} = 0.15$

$\Rightarrow S P - C P_{1} = 0.15 \times C P_{1}$
$\Rightarrow S P - C P_{1} = 0.15 C P_{1} + C P_{1}$

$\Rightarrow$ $S P = 1.15 \times C P_{1}$

$\Rightarrow$ $C P_{1} = \frac{100}{115} \times S P$ ... (1)

For the second article,

Given, loss $% = 15 %$
Loss $% = \frac{C P_{2} - S P}{C P_{2}} \times 100 = 15 %$
$\Rightarrow \frac{C P_{2} - S P}{C P_{2}} = 0.15$

$\Rightarrow C P_{2} - S P = 0.15 \times C P_{2}$
$\Rightarrow C P_{2} - 0.15 \times C P_{2} = S P$

$\Rightarrow 0.85 \times C P_{2} = S P$

$\Rightarrow C P_{2} = \frac{100}{85} \times S P$ ... (2)
and $S P = \frac{85}{100} \times C P_{2}$
$= 0.85 \times C P_{2}$

From equations (1) and (2),

$\Rightarrow 1.15 \times C P_{1} = 0.85 \times C P_{2}$

$\Rightarrow C P_{1} = \frac{0.85}{1.15} \times C P_{2}$

$\Rightarrow C P_{1} = \frac{17}{23} \times C P_{2}$

$∴$ Total $C P = C P_{1} + C P_{2}$
$= \frac{17}{23} \times C P_{2} + C P_{2}$
$= \frac{40}{23} \times C P_{2}$

and Total $S P = 2 \times S P$ of each article

$= 2 \times (0.85 \times C P_{2}) = \frac{17}{10} \times C P_{2}$

And Total Loss $% = \frac{T o t a l C P - T o t a l S P}{T o t a l C P}$
$= \frac{\frac{40}{23} \times C P_{2} - \frac{17}{10} \times C P_{2}}{\frac{40}{23} \times C P_{2}} \times 100$
$= \frac{\frac{9}{230}}{\frac{40}{23}} \times 100$
$= 2.25 %$

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