In a game of 80 points, X can give Y 5 points and Z 15 points. How many points can Y give Z in a game of 75 points?
Correct Answer: Option B
Given that, in a game of 80 points, X can give Y 5 points and Z 15 points, i.e.
Number of points of Y = 80 – 5 = 75
Number of points of z = 80 – 15 = 65
\(\frac{x}{y} = \frac{{80}}{{75}}\) ------- (1)
\(and\frac{x}{z} = \frac{{80}}{{65}}\) ----------- (2)
Dividing (1) by (2), we obtain
\(\frac{y}{z} = \frac{{75}}{{65}}\)
Multiplying and dividing with 75, we get
\(\begin{array}{l} \frac{y}{z} = \frac{{75}}{{65}} \times \frac{{75}}{{75}}\\ \Rightarrow \frac{y}{z} = \frac{{75}}{{65}}\\ \Rightarrow \frac{{75}}{y} = \frac{{65}}{z} \end{array}\)
Thus Y can give Z : 75 – 65 = 10 points.
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