P$12\mathrm{.}3$ A timber beam $150$ mm wide by $300$ mm deep is reinforced by a steel plate $150$ mm wide and $12$ mm thick which is securely attached to its lower surface. Determine the percentage increase in the moment of resistance of the beam produced by the steel$-$reinforcing plate. The allowable stress in the timber is $12\frac{N}{m}{m}^2$ and in the steel, $155\frac{N}{m}{m}^2.$ The modular ratio is $20.$

Ans. $176\%.$