a man marks his good at a price that would give him 20% profit. he sells 3/5 of the goods at the marked price and sells the remaining at 20% discount. find his gain % on the whole transaction.
let the CP of the articles be 100
MP of the articles=100+20% of 100=120
total cpf x articles =100x
Let No,of artiles be x
SP of 3/5 of x=120
total SP of 3/5th articles=120*3/5*x=72x
SP of remaining articles:
Remaining aricles=1-3/5=2/5
SP of 2/5 of x= MP-20% of MP
=120-20%*120
=96
total SP of 2/5 articles=96*2/5*x
=38.4x
NetSP=72x+38.4=110.4x
profit=SP-CP=110.4x-100x
=10.4x
profit%=p/cp*100=(10.4/100)*100=10.4%
To find the gain percentage on the whole transaction, we need to consider the profits made from selling 3/5 of the goods at the marked price and the remaining goods at a 20% discount.
Let's consider the values given in the problem:
The man marks his goods at a price that would give him a 20% profit.
This means that the marked price of the goods is 120% of the cost price (100% + 20% profit).
He sells 3/5 of the goods at the marked price.
This means he sells 3/5 * 100% = 60% of the goods at the marked price.
Now, let's calculate the gain percentage step by step.
Step 1: Calculate the selling price of 3/5 of the goods.
Since he sells 3/5 of the goods at the marked price, the selling price is the same as the marked price, which is 120% of the cost price.
Selling price of 3/5 of the goods = 120% of the cost price
Step 2: Calculate the selling price of the remaining goods.
He sells the remaining goods at a 20% discount.
This means the selling price of the remaining goods is 100% - 20% = 80% of the cost price.
Selling price of the remaining goods = 80% of the cost price
Step 3: Calculate the total selling price of all the goods.
To find the total selling price, we need to sum up the selling price of 3/5 of the goods and the selling price of the remaining goods.
Total selling price = (Selling price of 3/5 of the goods) + (Selling price of the remaining goods)
Step 4: Calculate the total cost price of all the goods.
Since the selling price is given as a percentage of the cost price, we can find the total cost price by dividing the total selling price by the selling price percentage (120% or 1.2).
Total cost price = Total selling price / Selling price percentage (1.2)
Step 5: Calculate the overall gain percentage.
To find the gain percentage on the whole transaction, we can use the formula:
Overall gain percentage = ((Total selling price - Total cost price) / Total cost price) * 100
Substitute the values calculated in the previous steps to calculate the overall gain percentage.
Finally, compute the value and determine the man's gain percentage on the whole transaction.