Question : A man starts from place P and reaches place Q in 7 hours. He travels $\frac{1}{4}$th of the distance at 10 km/hr and the remaining distance at 12 km/hr. The distance between P and Q is:
Option 1: 72 km
Option 2: 90 km
Option 3: 80 km
Option 4: 70 km
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Correct Answer: 80 km
Solution :
Given: Time taken to reach from P to Q = 7 hours
Speed for the $\frac{1}{4}$
th
of the distance = 10 km/hr
Speed for the remaining distance = 12 km/hr
Let the distance be $4x$ km.
According to the given condition,
$\frac{x}{10}+\frac{3x}{12}=7$
⇒ $\frac{6x+15x}{60}=7$
⇒ $21x=7×60$
⇒ $x=\frac{7×60}{21}$
⇒ $x=20$
So, the total distance = 20 × 4 = 80 km
Hence, the correct answer is 80 km.
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