Page 170 - ICSE Math 8

According to the question, 5x – 2(100 – x) = 220
fi 5x – 200 + 2x = 220 fi 7x – 200 = 220

fi 7x = 220 + 200 = 420 (Transposing –200 to RHS)
7x 420
fi = fi x = 60 (Dividing both sides by 7)
7 7
So, the student attempted 60 questions correctly.

Example 13: 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
–1
4 km h , find the distance between the two towns.
–1
Solution: Let the speed of the steamer in still water be x km h .
Speed of stream = 4 km h –1
\ Speed upstream = Speed in still water – Speed of stream = (x – 4) km h –1
Speed downstream = (x + 4) km h –1
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 fi 5x = 180 (Transposing 20x to LHS and –100 to RHS)

5 180
fi x = fi x = 36 (Dividing both sides by 5)
5 5
\ Distance between the two towns = 20 × (36 + 4) km = (20 × 40) km = 800 km
–1
Example 14: A train is travelling at a speed of 60 km h from Delhi to Kolkata. On its return journey, it
–1
travels at a speed of 50 km h and takes 5 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 + 5) hour
\ Distance = 50 × (t + 5) km ...(2)
From (1) and (2), we have
60t = 50(t + 5) fi 60t = 50t + 250

fi 60t – 50t = 250 fi 10t = 250 (Transposing 50t to LHS)
10t 250
fi = fi t = 25 hours (Dividing both sides by 10)
10 10
\ Distance between Delhi and Kolkata = 60 × t = 60 × 25 = 1,500 km

Example 15: Each side of a triangle is increased by 10 cm. If the ratio of the perimeter of the new triangle
to the given triangle is 5 : 4, find the perimeter of the given triangle.

Solution: Let the perimeter of the given triangle be x cm.
If a, b, c are the three sides of the given triangle, then a + b + c = x ...(1)

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