CAT 2018

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Ratio and Proportion — Setting up linear equations from ratio conditions
• Formula: $$\frac{a + x}{b + x} = \frac{p}{q} \implies q(a + x) = p(b + x)$$

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2. Calculation

Let the original scores of Amal and Bimal be $11k$ and $14k$ respectively, where $k$ is a positive constant.

Let the equal increase in both scores after the appeal be $x$.

So the new scores become: Amal $= 11k + x$ and Bimal $= 14k + x$.

We are given that the new scores are in the ratio $47 : 56$, so:

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

Cross-multiplying:

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

$$616k + 56x = 658k + 47x$$

$$56x - 47x = 658k - 616k$$

$$9x = 42k$$

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

Now, Bimal's new score $= 14k + \frac{42k}{9} = \frac{126k + 42k}{9} = \frac{168k}{9}$

Bimal's original score $= 14k = \frac{126k}{9}$

Ratio of Bimal's new score to his original score:

$$\frac{\frac{168k}{9}}{\frac{126k}{9}} = \frac{168k}{126k} = \frac{168}{126} = \frac{4}{3}$$

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3. Solution

Answer = Option A ✅

The ratio of Bimal's new score to his original score is $\mathbf{4 : 3}$.