Question : Menu and Daya travel from point A to B, a distance of 105 km, at speeds of 10 km/hr and 25 km/hr, respectively. Daya reaches point B first and returns immediately and meets Menu at point C. Find the distance from point A to point C.
Option 1: 35 km
Option 2: 60 km
Option 3: 45 km
Option 4: 62 km
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Correct Answer: 60 km
Solution :
The distance of A and B = 105 km
Let's assume that they meet at point C, and CB = $x$
Then AC = $(105 - x)$
Speed of Daya = 25 km/hr
Speed of Menu = 10 km/hr
Distance covered by Daya = $(105 + x)$ km
Menu covers $(105 - x)$ km
Since, Time = $\frac{\text{Distance}}{\text{Speed}}$
So, $\frac{105+x}{ 25}=\frac{105-x}{ 10}$
⇒ $1050 + 10x = 2625 - 25x$
⇒ $35x = 1575$
⇒ $x = 45$
So, distance from point A to point C = (105 - 45) = 60 km
Hence, the correct answer is 60 km.
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