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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Question : A car starts from point A towards point B, travelling at the speed of 20 km/hr. $1\frac{1}{2}$ hours later, another car starts from the point and travels at the speed of 30 km/hr and reaches $2\frac{1}{2}$ hours before the first car. Find the distance between A and B.
Question : Amita travels from her house at $3 \frac{1}{2}$ km/hr and reaches her school 6 minutes late. The next day she travels at $4 \frac{1}{2}$ km/hr and reaches her school 10 minutes early. What is the distance between her house and the school?
Question : A man travels $\frac{3}{4}$th of the distance of his journey by bus, $\frac{1}{6}$th by rickshaw and the remaining 2 km on foot. The total distance travelled by the man is:
Question : A person travels 600 km by train at 80 km/hr, 800 km by ship at 40 km/hr, 500 km by aeroplane at 400 km/hr, and 100 km by car at 50 km/hr. What is the average speed for the entire distance?
Question : A man travels 50 km at 25 km/hr, the next 40 km at 20 km/hr, and then 90 km at 15 km/hr. His average speed is:
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