Eight charges having values as shown in figure are arranged symmetric…

The correct answer is Option (1) → \( 2.43 \times 10^{6}\,\mathrm{V} \)

Electric potential is a scalar, so the potentials of the eight charges simply add, with their signs. All the charges are at the same distance \( r \) from O, so

    \( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 + q_2 + \dots + q_8}{r} \)

Readings from the figure (in \( \mu\mathrm{C} \)):

    \( q_{\mathrm{total}} = -7 - 1 + 3 - 5 + 10 + 15 + 7 + 5 = +27\,\mu\mathrm{C} = 27\times10^{-6}\,\mathrm{C} \)
    \( r = 10\,\mathrm{cm} = 0.1\,\mathrm{m} \)

    \( \displaystyle V = \frac{9\times10^{9} \times 27\times10^{-6}}{0.1} = 2.43\times10^{6}\,\mathrm{V} \)

The symmetric arrangement does not matter for the potential; only the algebraic sum of the charges does.