One-third of goods are sold at a 15% profit. 25% of the goods are sold at a 20% profit and the rest at a 20% loss. If the total profit of ₹138.50 is earned on the whole transaction, then the value(in ₹) of the goods is:

Let the total goods be 300

One third, means 100 goods are sold at 15℅ profit

25℅ means 75 goods are sold at 20℅ profit

The rest, means 125 goods are 20℅ loss

Let the price of each good be Re. 1

So, now calculating the profit and loss amounts:

For 100 goods, profit is 15℅ = Rs. 115

For 75 goods, profit is 20℅ = Rs. 90

For 125 goods, loss is 20℅ = Rs. 100

So, total amount of the selling price= Rs. 305

Total cost price = Rs.300

So, the profit = Selling price- cost price = Rs. 305-300 = Rs.5

Now equating it to the real values:

Rs. 5 is the profit when total amount of goods is Rs 300.

Rs. 138.50 is the profit when total amount of goods is= (300/5)*138.5 = Rs. 8310

$$\therefore$$ The value of the goods is Rs. 8310.