Page 104 - ICSE Math 8

Example 7: Honey can paint a shirt in 15 days and Kini can paint the same shirt in 30 days. If they work
together, in how many days will the shirt be painted?
Solution: Honey can paint the shirt in 15 days.
1
\ Honey’s 1 day work =
15
Kini can paint the shirt in 30 days.
1
\ Kini’s 1 day work =
30
\ Honey’s and Kini’s 1 day work = 1 + 1 = 21+ = 3 = 10
15 30 30 30 1
1
If Honey and Kini work together, of the work is completed in 1 day.
10
1 10
\ 1 work will be completed in 1 ÷ days = 1 × = 10 days.
10 1
Hence, Honey and Kini can together paint the shirt in 10 days.

Example 8: Ram and Shyam can together paint a wall in 25 minutes. Ram can alone paint the same wall
in 50 minutes. They work together for 20 minutes, then Ram goes away. In how many minutes
will Shyam paint the remaining part of the wall?

Solution: Ram and Shyam can together paint a wall in 25 minutes.
1
\ Ram’s and Shyam’s 1 minute work =
25
Ram can alone paint the wall in 50 minutes. \ Ram’s 1 minute work = 1
50
\ Shyam’s 1 minute work = (Ram’s and Shyam’s 1 minute work) – (Ram’s 1 minute work)

1 1 21− 1
= − = =
25 50 50 50
1
The amount of work that can be done by Ram and Shyam in 20 minutes = 20 × 25 = 4
5
4 1
Remaining work = 1 – =
5 5
1
Shyam can complete of the work in 1 minute.
50
1
\ Shyam can complete 1 work in 1 ÷ 50 minute = 1 × 50 minutes = 50 minutes
1
1 1
Hence, of remaining work will be completed by Shyam in 50 × = 10 minutes
5 5
\ Shyam will paint the remaining part of the wall in 10 minutes.
Example 9: Spinning 4 hours daily, Santosh can spin 3 kg of cotton balls in 15 days. If she spins 5 hours
daily, how many days will she take to spin 8 kg of cotton balls?
Solution: Spinning 4 hours daily, Santosh can spin 3 kg of cotton balls in 15 days.
15
\ Spinning 4 hours daily, Santosh can spin 1 kg of cotton balls in = 5 days
3
fi Spinning 1 hour daily, Santosh can spin 1 kg of cotton balls in 5 × 4 = 20 days
fi Spinning 1 hour daily, Santosh can spin 8 kg of cotton balls in 20 × 8 = 160 days
160
fi Spinning 5 hours daily, Santosh can spin 8 kg of cotton balls in = 32 days
5
Hence, if Santosh spins 5 hours daily, she will take 32 days to spin 8 kg of cotton balls.

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