Page 163 - Start Up Mathematics_8 (Non CCE)

Example 3: Madhu and Meena can do a piece of work in 9 hours. Meena and Mamta can do it in 12 hours
and Madhu and Mamta can do it in 18 hours. In how many hours will they finish the work
together and separately?
Solution: Madhu and Meena can do the work in 9 hours.
1
\ (Madhu’s + Meena’s) 1 hour work = ...(1)
9
Meena and Mamta can do the work in 12 hours.
1
\ (Meena’s + Mamta’s) 1 hour work = ...(2)
12
Madhu and Mamta can do the work in 18 hours.
1
\ (Madhu’s + Mamta’s) 1 hour work = ...(3)
18
Adding (1), (2) and (3), we get
1
2(Madhu’s + Meena’s + Mamta’s) 1 hour work = + 1 + 1 = 43 2++ = 9 = 1
9 12 18 36 36 4
1
\ (Madhu’s + Meena’s + Mamta’s) 1 hour work =
1 8
fi Madhu, Meena and Mamta can do of the work in 1 hour.
8
1 8
\ Madhu, Meena and Mamta can do 1 work in 1 ÷ hours = 1 × hours = 8 hours
8 1
Hence, Madhu, Meena and Mamta can together finish the work in 8 hours.
Now, Madhu’s 1 hour work alone = (Madhu’s + Meena’s + Mamta’s) 1 hour work
– (Meena’s + Mamta’s) 1 hour work

1 1 32- 1
= - = =
8 12 24 24
1
Madhu can alone do of the work in 1 hour.
24

Madhu can alone do 1 work in 1∏ 1 hours = 1 ¥ 24 = 24 hours
24 1
\ Madhu can alone finish the work in 24 hours.
Meena’s 1 hour work = (Madhu’s + Meena’s + Mamta’s) 1 hour work –
(Madhu’s + Mamta’s) 1 hour work
1 1 94- 5
= - = =
8 18 72 72

5
Meena can alone do of the work in 1 hour
72 5 72 2
\ Meena can alone do 1 work in 1 ÷ hours = 1 ¥ hours = 14 hours
72 5 5

2
So, Meena can finish the work in 14 hours.
5
Mamta’s 1 hour work = (Madhu’s + Meena’s + Mamta’s) 1 hour work
– (Madhu’s + Meena’s) 1 hour work
1 1 98- 1
= - = =
8 9 72 72

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