Page 146 - Start Up Mathematics_8 (Non CCE)

fi 25x = 45(2,170 – x) (Multiplying both sides by 1,000)

fi 25x = 45 × 2,170 – 45x
fi 25x + 45x = 45 × 2,170 (Transposing –45x to LHS)
fi 70x = 45 × 2,170

70x 45 ¥ 2 170,
fi = (Dividing both sides by 70)
70 70
fi x = 45 × 31 = 1,395
So, the required numbers are 1,395 and (2,170 – 1,395), i.e., 1,395 and 775.
Example 18: A steamer going downstream in a river covers the distance between two towns in 20 hours.
While moving upstream, it covers the same distance in 25 hours. If the speed of the stream
is 4 km/h, find the distance between the two towns. (NCERT)
Solution: Let the speed of the steamer in still water be x km/h.
Speed of stream = 4 km/h
\ Speed upstream = Speed in still water – Speed of stream = (x – 4) km/h

Speed downstream = (x + 4) km/h
Time upstream = 25 hours
Time downstream = 20 hours
Distance upstream = Speed upstream × Time upstream = 25 × (x – 4) km

Distance downstream = Speed downstream × Time downstream = 20 × (x + 4) km
Now, distance upstream = distance downstream
fi 25 × (x – 4) = 20 × (x + 4)
fi 25x – 100 = 20x + 80
fi 25x – 20x = 80 + 100 (Transposing 20x to LHS and –100 to RHS)

fi 5x = 180
5 180
fi x = (Dividing both sides by 5)
5 5
fi x = 36
\ Distance between the two towns = 20 × (36 + 4) km = (20 × 40) km = 800 km

Example 19: A train is travelling at a speed of 60 km/h from Delhi to Kolkata. On its return journey, it
travels at a speed of 50 km/h and takes 4 hours more than the onward journey. What is the
distance between Delhi and Kolkata?
Solution: Let t be the time of onward journey.
We know that, Distance = Speed × Time

For the onward journey, i.e, Delhi to Kolkata
Distance = (60 × t) km ...(1)
On the return journey, i.e., Kolkata to Delhi
Time = (t + 4) hour
\ Distance = 50 × (t + 4) km ...(2)

From (1) and (2), we have
60t = 50(t + 4)

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