a man sells two tables at the same price. On one he makes profit of 10% and on other he suffers a loss of 10 %.Find his loss or gain percent on the whole transaction
Profit of 10% = 100% + 10% = 110%
Loss of 10% = 100% - 10% = 90%
Let selling price of each table be x
Total selling price = 2 x
Total cost price = 100 x /110 + 100 x / 90 =
9 * 100 x / ( 11 * 90 ) + 100 * 11 x / ( 90 * 11 ) =
900 x / 990 + 1100 x / 990 =
2000 x / 990 =
10 * 200 x / ( 10 * 99 ) =
= 200 x / 99
Loss = 200 x / 99 - 2 x =
200 x / 99 - 2 * 99 x / 99 =
200 x / 99 - 198 x / 99 =
2 x / 99
Loss percentage = [ ( 2 x / 99 ) / 200 x / 99 ] * 100% = ( 2 x / 200 x ) * 100% = 0.01 * 100% = 1%
OR
Profit * loss = 1.1 * 0.9 = 0.99 = 99 / 100 = 99%
100% - 99% = 1 %
To find the overall loss or gain percentage, we need to consider both the profit and loss percentages. Let's assume the selling price of each table is $100 for simplicity.
Table 1:
Profit percentage = 10%
Selling price = $100
Profit = 10% of $100 = $10
Table 2:
Loss percentage = 10%
Selling price = $100
Loss = 10% of $100 = $10
To find the overall loss or gain, we need to combine the profit and loss. Since both the profit and loss amount is $10, they cancel each other out, resulting in no overall loss or gain for the two tables.
So, the overall loss or gain percentage in this transaction is 0%. The man didn't experience any loss or gain on the whole transaction.
To solve this problem, we need to calculate the overall gain or loss percentage on the two tables.
Let's assume the selling price of each table is $100.
On the first table, the man makes a profit of 10%, which means he sells it for $110.
On the second table, the man suffers a loss of 10%, which means he sells it for $90.
Now let's calculate the overall result.
Total selling price = (Selling price of the first table) + (Selling price of the second table)
= $110 + $90
= $200
Total cost price = (Cost price of the first table) + (Cost price of the second table)
= (Selling price of the first table) + (Loss on the second table)
= $110 + ($100 - $90)
= $110 + $10
= $120
Now we can calculate the overall gain or loss percentage.
Overall gain or loss percentage = ((Total selling price - Total cost price) / Total cost price) × 100
= (($200 - $120) / $120) × 100
= ($80 / $120) × 100
= 66.67%
Therefore, the man had a gain of approximately 66.67% on the whole transaction.