Arithmetic

Ratio, Proportion & Variation

Medium

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

$5:4$

$3:2$

$8:5$

$4:3$

✅ Correct Option: 4

Let's assign variables to make this problem manageable. Since Amal and Bimal's original scores are in the ratio 11:14, we can write:

Amal's original score = $11x$

Bimal's original score = $14x$

When we have a ratio like 11:14, we can think of it as 11 parts to 14 parts. By using $11x$ and $14x$ , we maintain this ratio while keeping our work algebraic.

The problem states that both scores increase by the same amount. Let's call this increase $d$ .

After the increase:

Amal's new score = $11x + d$

Bimal's new score = $14x + d$

We're told the new scores are in the ratio 47:56. This means:

$\tfrac{\text{Amal's new score}}{\text{Bimal's new score}} = \tfrac{47}{56}$

Substituting our expressions:

$\tfrac{11x + d}{14x + d} = \tfrac{47}{56}$

Cross-multiplying gives us:

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

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

Collecting like terms:

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

$9d = 42x$

$d = \tfrac{42x}{9} = \tfrac{14x}{3}$

The increase for both students is $\tfrac{14x}{3}$ .

Now we can find Bimal's actual scores:

Original score: $14x$

New score: $14x + d = 14x + \tfrac{14x}{3} = 14x\left(1 + \tfrac{1}{3}\right) = 14x \times \tfrac{4}{3} = \tfrac{56x}{3}$

The ratio of Bimal's new score to his original score is:

$\tfrac{\text{New score}}{\text{Original score}} = \tfrac{\tfrac{56x}{3}}{14x} = \tfrac{56x}{3} \times \tfrac{1}{14x} = \tfrac{56}{42} = \tfrac{4}{3}$

Therefore, the ratio is 4:3.

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CAT Past Year Questions (Topic-Wise)

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