Question

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

• A. 5:4
• B. 8:5
• C. 4:3
• D. 3:2

Answer 1

The Correct Option is C

Step 1: Assume the Initial Scores

Given that the ratio of scores of Amal and Bimal is \( 11 : 14 \).\ Let the scores be:

\[ \text{Amal's score} = 11x, \quad \text{Bimal's score} = 14x \]

Step 2: Let a Score 'a' Be Added to Both

After adding \( a \) to both scores, the new ratio becomes:

\[ \frac{11x + a}{14x + a} = \frac{47}{56} \]

Step 3: Cross Multiply and Simplify

\[ 56(11x + a) = 47(14x + a) \]

\[ 616x + 56a = 658x + 47a \]

Bring like terms together:

\[ 56a - 47a = 658x - 616x \quad \Rightarrow \quad 9a = 42x \]

\[ a = \frac{42x}{9} \]

Step 4: Find the New Ratio of Amal to Bimal

Add \( a \) to Amal’s score only and compare with Bimal’s original score:

\[ \text{New Amal score} = 11x + a = 11x + \frac{42x}{9} = \frac{141x + 42x}{9} = \frac{183x}{9} \]

\[ \text{Ratio} = \frac{183x}{9} : 14x = \frac{183}{9} : 14 = 20.33 : 14 \]

But if we simplify directly using:

\[ \text{Required Ratio} = \left(14x + \frac{42x}{9} \right) : 14x = \frac{(126x + 42x)}{9} : 14x = \frac{168x}{9} : 14x \]

\[ \text{Divide both terms by } x: \quad \frac{168}{9} : 14 = \frac{168}{126} = \frac{4}{3} \]

Final Answer:

\[ \boxed{4 : 3} \]