A Comprehensive Analysis: Does the Vendor Gain or Lose from Selling Mangoes at Different Prices?

When dealing with market transactions, it is crucial to understand the underlying economics of the exchange to determine whether one gains or loses in the process. In this scenario, a vendor purchases mangoes at different prices and then sells them at another price. Let's delve into the detailed calculation to ascertain if the vendor gains or loses, and by what percentage.

Step-by-Step Calculation

Step 1: Cost Price Calculation

The vendor buys mangoes at two different rates: Rs. 10 for 15 mangoes and Rs. 10 for 25 mangoes. To find the cost price per mango, let's perform the calculation.

Buying Mangoes at Rs. 10 for 15 Mangoes:

Cost Price CP1 for 15 mangoes Rs. 10

Therefore, the cost for 1 mango frac14; (frac{10}{15}) frac23; (frac{2}{3}) Rs.

Buying Mangoes at Rs. 10 for 25 Mangoes:

Cost Price CP2 for 25 mangoes Rs. 10

Therefore, the cost for 1 mango frac14; (frac{10}{25}) frac25; (frac{2}{5}) Rs.

Step 2: Total Cost Price for the Same Number of Mangoes

Assuming the vendor buys n n mangoes at each price, the total number of mangoes bought n 2n.

Total cost for n n mangoes at frac23; (frac{2}{3}) Rs. each:

Total Cost 1 n n × frac23; (frac{2}{3}) frac23;n frac{2n}{3} Rs.

Total cost for n n mangoes at frac25; (frac{2}{5}) Rs. each:

Total Cost 2 n n × frac25; (frac{2}{5}) frac25;n frac{2n}{5} Rs.

Adding these costs together, we get the total cost price, CP:

Total CP frac23;n frac{2n}{3} frac25;n frac{2n}{5}

To add these fractions, we find a common denominator, which is 15:

frac23;n frac{2n}{3} frac14; (frac{10n}{15}) and frac25;n frac{2n}{5} frac14; (frac{6n}{15})

Adding them together:

Total CP frac14; (frac{10n}{15}) frac14; (frac{6n}{15}) frac14; (frac{16n}{15}) Rs.

Step 3: Selling Price Calculation

The vendor sells the mangoes at Rs. 20 for 40 mangoes. Let's calculate the selling price per mango:

Selling Price SP for 40 mangoes Rs. 20

Therefore, selling price for 1 mango frac14; (frac{20}{40}) frac12; (frac{1}{2}) Rs.

Calculating the total selling price for n 2n mangoes:

Total SP n 2n × frac12; (frac{1}{2}) n n Rs.

Step 4: Profit or Loss Calculation

Now we can determine if there is a gain or loss:

Profit/Loss Total SP - Total CP n n - frac14; (frac{16n}{15})

Calculating the difference:

Profit/Loss n n - frac14; (frac{16n}{15}) frac14; (frac{15n}{15}) - frac14; (frac{16n}{15}) frac14; -(frac{n}{15})

Since the result is negative, this indicates a loss.

Step 5: Percentage Loss Calculation

Let's find the percentage loss:

Percentage Loss lft; (left) frac14; (frac{text{Loss}}{text{Total CP}}) rft; (right) × 100 lft; (left) frac14; (frac{frac{n}{15}}{frac{16n}{15}}) rft; (right) × 100

Simplifying:

Percentage Loss lft; (left) frac14; (frac{1}{16}) rft; (right) × 100 6.25

Conclusion

The vendor incurs a loss of 6.25% from the transactions.

Understanding these calculations is vital for any business dealing with market fluctuations and pricing strategies to ensure financial stability and profitability.