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The scores of Amal and Bimal in an examination are in the ratio $11: 14$. After an appeal, their scores increase by the same amount and their new scores are in the ratio $47 : 56$. The ratio of Bimal's new score to that of his original score is

1. $5:4$
2. $8:5$
3. $4:3$
4. $3:2$

Given that, the ratio of Amal and Bimal scores is $11:14.$

• Let, the score of Amal $= 11x$
• Then, the score of Bimal $= 14x$
• Where $x$ is some constant.

Let their scores increases by $k.$

So, $\frac{11x+k}{14x+k} = \frac{47}{56}$

$\Rightarrow 56(11x+k) = 47(14x+k)$

$\Rightarrow 616x+56K = 658x+47k$

$\Rightarrow 56k – 47k = 658x – 616x$

$\Rightarrow 9k = 42x$

$\Rightarrow \boxed{k = \frac{42}{9}x}$

Now, the score of Bimal:

• Bimal new score $= 14x + k = 14x + \frac{42}{9}x$
• Bimal original score $= 14x$

$\therefore$ The ratio of Bimal’s new score to that of his original score $= \frac{14x+\frac{42x}{9}}{14x} = \frac{14x \left(1+\frac{3}{9} \right)}{14x}= \frac{9+3}{9} = \frac{12}{9} = \frac{4}{3}$

Therefore, the ratio of Bimal's new score to that of his original score is $4:3.$

Correct Answer $: \text{C}$

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