Two cows were sold for $R s . 12, 000$ each, one at a gain of $20$ % and the other at a loss of $20$ %. Find the loss or gain in the entire transaction.

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Solution

We first find out the cost price of each cow and then add them to find the total amount spent. We know the total money received. Comparing them, we will know whether there is a loss or gain in the whole transaction.
First Cow:
$S . P . = R s . 12, 000$ .
$G a i n = 20$ %. Therefore,
Cost price $= \frac{100}{(100 + g a i n)} \times S . P .$
$= \frac{100}{(100 + 20)} \times 12000$
$= \frac{100}{120} \times 12000$
$= 10000$ . Second Cow:
$S . P . = R s . 12, 000$ .
$L o s s = 20$ %. Therefore,
Cost price $= \frac{100}{(100 - l o s s)} \times S . P .$
$= \frac{100}{(100 - 20)} \times 12000$
$= \frac{100}{80} \times 12000$
$= 15000$ .
Therefore, the total cost price is $10000 + 15000 = 25000$
And total selling price is $12000 \times 2 = 24000$
Thus, cost price greater than selling price.
Hence, there is a loss of Rs. $1000$ .

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Two cows were sold for Rs.12,000 each, one at a gain of 20% and the other at a loss of 20%. Find the loss or gain in the entire transaction.

Two cows were sold for $R s . 12, 000$ each, one at a gain of $20$ % and the other at a loss of $20$ %. Find the loss or gain in the entire transaction.