A man sells his goods at a certain price, 20% of which is his profit. If the price at which he buys the goods increases by 10% and he sells them at an 8% higher price, then what will be his profit percent (correct to one decimal place)?

Solution (By Examveda Team)

Let's assume that the cost price of the goods for the man is Rs. 100.
Given:
Profit = 20% of the selling price
Cost Price = Rs. 100
Profit = 20% of Selling Price
Profit = 0.2 × Selling Price
Selling Price = Cost Price + Profit
Selling Price = Rs. 100 + 0.2 × Selling Price
0.8 × Selling Price = Rs. 100
Selling Price = $$\frac{{{\text{Rs}}{\text{. }}100}}{{0.8}}$$
Selling Price = Rs. 125
So, the man sells the goods at Rs. 125.
Now, after the price at which he buys the goods increases by 10%, the new cost price will be:
New Cost Price = Rs. 100 + 10% of Rs. 100
New Cost Price = Rs. 100 + Rs. 10
New Cost Price = Rs. 110
He sells the goods at an 8% higher price, so the new selling price will be:
New Selling Price = Rs. 125 + 8% of Rs. 125
New Selling Price = Rs. 125 + Rs. 10
New Selling Price = Rs. 135
New Profit = New Selling Price - New Cost Price
New Profit = Rs. 135 - Rs. 110
New Profit = Rs. 25
Now, let's calculate the profit percentage based on the new selling price and the new cost price:
Profit Percentage = $$\frac{{{\text{Profit}}}}{{{\text{Cost Price}}}} \times 100$$
Profit Percentage = $$\frac{{25}}{{100}} \times 100$$
Profit Percentage ≈ 22.7%
Therefore, the man's profit percentage, correct to one decimal place, is approximately 22.7%.