A brass plate with a surface area of 200 cm^2 on one side is...

Total surface area to be electroplated (both sides) $= 2 \times 200 = 400 \text{ cm}^2$

Thickness of the silver layer $= 0.10 \text{ mm} = 0.01 \text{ cm}$

Volume of silver deposited $= \text{Area} \times \text{Thickness} = 400 \times 0.01 = 4 \text{ cm}^3$

Mass of silver deposited, $m = \text{Volume} \times \text{Density} = 4 \times 10.5 = 42 \text{ g}$

According to Faraday's first law of electrolysis:

$m = \dfrac{M}{nF} I t$

For silver, the valency $n = 1$. Substituting the given values:

$42 = \dfrac{107.9}{1 \times 96500} \times 15 \times t$

$t = \dfrac{42 \times 96500}{107.9 \times 15} \text{ s}$

Converting the time into minutes:

$t = \dfrac{42 \times 96500}{107.9 \times 15 \times 60} \text{ min}$

$t = \dfrac{4053000}{97110} \text{ min} \approx 41.73 \text{ min}$

Rounding off to the nearest integer, the time taken is approximately $42 \text{ minutes}$.