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Phrases Distance And Direction PYQ

One day, Amit left home and cycled 15 km southwards, turned right and cycled 7 km and turned right andcycled 10 km and turned left and cycled 5 km. How many kilometers will he have to cycle to reach his home?





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Solution

Given:

  • Amit cycled 15 km south.
  • Then turned right (west) and cycled 7 km.
  • Turned right again (north) and cycled 10 km.
  • Finally, turned left (west) and cycled 5 km.

Calculation:

Vertical displacement: 15−10=5km (south)
Horizontal displacement: 7+5=12km (west)
Using Pythagoras theorem:
Distance = √(5² + 12²) = √(25 + 144) = √169 = 13 \, \text{km}

Answer:

Amit needs to cycle 13 km to return home.


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