Ratio of new score to original score

Let original scores of Amal and Bimal be $11x$ and $14x$. Let the increase in score for each be $k$. New ratio: $\frac{11x + k}{14x + k} = \frac{47}{56}$.

Cross-multiplying: $56(11x + k) = 47(14x + k)$ $616x + 56k = 658x + 47k$ $9k = 42x \implies k = \frac{14}{3}x$

Bimal's original score $= 14x$. Bimal's new score $= 14x + k = 14x + \frac{14}{3}x = \frac{56}{3}x$.

Ratio of Bimal's new score to original score $= \frac{\frac{56}{3}x}{14x} = \frac{56}{42} = \frac{4}{3} = 4 : 3$.