Define Base Values

Let the actual selling price (SP) be 14 units. Selling at $\frac{5}{14}$ of this price means the new selling price ($SP_1$) is 5 units.

$SP_1 = 14 \times \frac{5}{14} = 5$

Calculate Cost Price (CP)

Since selling for 5 units results in a 20% loss, the Cost Price is calculated using the loss percentage formula where $SP = CP \times (1 - 0.20)$.

$CP = \frac{5}{0.8} = 6.25$

Find New Selling Price

The second scenario is selling at 80% of the actual selling price (14 units).

$SP_2 = 14 \times 0.8 = 11.2$

Calculate Profit Percentage

The profit is the difference between $SP_2$ and $CP$. Profit percentage is $\frac{\text{Profit}}{CP} \times 100$.

$\text{Profit}\% = \frac{11.2 - 6.25}{6.25} \times 100 = \frac{4.95}{6.25} \times 100 = 79.2\%$