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A dealer sold two types of goods for 10000 each. One of them he lost 20% and on the other he gained 20%. Find his gain or loss percent in the entire transaction.
Given :
A dealer sold two types of goods for 10000 each.
One of them he lost 20% and on the other, he gained 20%.
To do :
We have to find the loss or gain % in the whole transaction.
Solution :
Let the cost price of the first item be 'a', and sold it for a 20% loss.
The selling price of the first item $= ₹10000$
Since it sold for a loss of 20%, $80$% of a $=10000$
$\frac{80}{100} a = 10000$
$\frac{4}{5} a = 10000$
$a = 10000 \times \frac{5}{4}$
$a = 12500$
Therefore, the cost price of the first item$=12500$.
Let the cost price of the second item be 'b', and sold it for 20% profit.
The selling price of the second item $= ₹10000$
Since it sold for a profit of 20%, $120$% of b $=10000$
$\frac{120}{100} b = 10000$
$\frac{6}{5} b = 10000$
$a = 10000 \times \frac{5}{6}$
$a = 8333$
Therefore, the cost price of the second item$=8333$.
The total cost price $= 12500 + 8333 = 20833$
Total selling price $=10000 + 10000 = 20000$
The amount Loss $=$ Total cost price $-$ Total selling price
$ = 20833 - 20000 = 833$
Loss % $= \frac{833}{20000} \times 100$
$ = 4.165$
Therefore, there was a loss of 4.165% on the entire transaction.
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