Question : A man travels 450 km to his home, partly by train and partly by car. It takes 8 hours and 40 minutes if he travels 240 km by train and rests by car. It takes 20 minutes more if he travels 180 km by train and the rest by car. The speed of the car in km/h is:
Option 1: 45
Option 2: 50
Option 3: 60
Option 4: 48
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Correct Answer: 45
Solution : Let the speed of the train and the car be $a$ km/h and $b$ km/h, respectively. According to the question, $\frac{240}{a}+\frac{450–240}{b}=8\frac{40}{60}$ ⇒ $\frac{240}{a}+\frac{210}{b}=\frac{26}{3}$ ---------------------------(equation 1) Also, $\frac{180}{a}+\frac{450–180}{b}=9$ ⇒ $\frac{180}{a}+\frac{270}{b}=9$ --------------------------------------(equation 2) Multiply equation 1 by 3 and equation 2 by 4 we get, $\frac{720}{a}+\frac{630}{b}=26$ --------------------------------------(equation 3) $\frac{720}{a}+\frac{1080}{b}=36$ ------------------------------------(equation 4) Now subtracting equation 3 from equation 4 we get, ⇒ $\frac{450}{b}=10$ ⇒ $b=45$ km/h Hence, the correct answer is 45.
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Question : A man travels 404 kilometres, partly by train and steamer. He spends 10 hours more time on the steamer. If the speed of the steamer is 30 km/hr and the velocity of the train is 50 km/hr, how much distance does he cover by steamer?
Question : A car travels 80 km in 2 hours, and a train travels 180 km in 3 hours. The ratio of the speed of the car to that of the train is:
Question : A man travels for 14 hours and 40 minutes. He covers half of the journey by train at a rate of 60 km/hr and the rest by road at a rate of 50 km/hr. The distance travelled by him is:
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