[20 points] In a game A can give B 20 points in 60 and C 18 points in 90. How many points can C give B in a game

For Competitive Exams

In a game A can give B 20 points in 60 and C 18 points in 90. How many points can C give B in a game of 120?

20 points

22 points

18 points

40 points

Explanation:

A can give C 18 points in 90

=> While A scores 90 points, C scores $\left(90-18\right)$=72 points

$\text{=> While A scores }\dfrac{90}{72}\text{ points, C scores 1 point.}$

$\text{=> While A scores }\dfrac{90}{72} \times 120 =\dfrac{90}{6} \times 10\text{ = 150 points, C scores 120 point.}$

A can give B 20 points in 60

=> While A scores 60 points, B scores $\left(60-20\right)$=40 points

$\text{=> While A scores 1 point, B scores }\dfrac{40}{60} = \dfrac{2}{3}\text{ points}$

$\text{=> While A scores 150 points, B scores }\dfrac{2}{3} \times 150 = 100\text{ points}$

i.e., while C scores 120 points, B scores 100 points

Hence, in a 120 race, C can give B $\left(120-100\right)$=20 points

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