Two articles are sold for Rs. 840 and Rs. 960 at 20% gain and 4% loss respectively. What is overall gain or loss percentage.

Article 1 is sold for Rs. 840 at a 20% gain.

Article 2 is sold for Rs. 960 at a 4% loss.

Gain or Loss percentage formula:

​$$\text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain \%}}{100}\right) \quad \text{or} \quad \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right)$$​​

Overall Gain/Loss percentage:

​$$\text{Overall Gain/Loss \%} = \frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \times 100$$​​

For Article 1 (20% gain):

​$$\text{SP}_1 = \text{CP}_1 \times \left(1 + \frac{20}{100}\right) = \text{CP}_1 \times 1.2 \\ \ 840 = \text{CP}_1 \times 1.2\\\\\\text{CP}_1 = \frac{840}{1.2} = 70$$​​

For Article 2 (4% loss):

​$$\text{SP}_2 = \text{CP}_2 \times \left(1 - \frac{4}{100}\right) = \text{CP}_2 \times 0.96 \\960 = \text{CP}_2 \times 0.96 \\\text{CP}_2 = \frac{960}{0.96} = 1000$$​​

Total CP = 700 + 1000 = 1700

Total SP = 840 + 960 = 1800

Overall gain:

Gain = 1800 - 1700 = 100

​$$\text{Overall Gain \%} = \frac{100}{1700} \times 100 = 5\frac{15}{17}\%$$​​

Thus, The overall gain is $$\bf 5\frac{15}{17}\%$$​​