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प्रश्न
Places A and B are 160 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.
Places A and B are 160 km apart on a highway. One car starts from A and another from B at the same time. If they travel in the same direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.
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उत्तर
Let the speed of the car A and B be x km/h and y km/h respectively. Let x > y.
Case-1: When they travel in the same direction
From the figure
AC – BC = 160
⇒ x × 8 – y × 8 = 160
⇒ x – y = 20
Case-2: When they travel in opposite direction
From the figure
AC + BC = 160
⇒ x × 2 + y × 2 = 160
⇒ x + y = 80
Adding (i) and (ii), we get
2x = 100
⇒ x = 50 km/h
Putting x = 50 in (ii), we have
50 + y = 80
⇒ y = 80 – 50
⇒ y = 30 km/h
Hence, the speeds of the cars are 50 km/h and 30 km/h.
