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Example 17: Shreya can paint a wall in 6 hours. What part of the wall will she paint in 2 hours?

Solution: Wall painted by Shreya in 6 hours = 1 (One whole)
1
So, the wall painted by Shreya in 1 hour = part of the wall
6
Thus, the wall painted by Shreya in 2 hours = 1 × 2 = 1 part of the wall
6 3
Example 18: Aman can do a piece of work in 15 days and Raman can do it in 20 days. If both of
them work together, how long will they take to complete it?
Solution: Time taken by Aman to complete a whole (1) work = 15 days
1
So, the work done by Aman in 1 day =
15
Time taken to complete a whole (1) work by Raman = 20 days
1
So, the work done by Raman in 1 day =
20
So, work done by Aman and Raman together in 1 day = 1 + 1 = 4 + 3 = 7
15 20 60 60
Now, 7 part of the work is completed by Aman and Raman together in 1 day.
60
4
Thus, they together will complete the whole work in 60 days, i.e., 8 days.
7 7
Example 19: A and B can do a work in 18 days, B and C can do it in 24 days, and C and A can do it in 36 days.
(a) In how many days can A, B, and C complete the work together?
(b) In how many days can B alone complete the work?

Solution: (a) Time taken by A and B to complete the work = 18 days
1
So, (A + B)’s 1 day’s work =
18
Time taken by B and C to complete the work = 24 days
1
So, (B + C)’s 1 day’s work =
24
Time taken by C and A to complete the work = 36 days

1
So, (C + A)’s 1 day’s work =
36
1 1 1 4 + 3 + 2 9 1
So, 2(A + B + C)’s 1 day’s work = + + = = =
18 24 36 72 72 8
1
So, (A + B + C)’s 1 day’s work =
16
Thus, A, B, and C together can complete the work in 16 days.

(b) Work done by B in 1 day = Work done by A, B, and C together in 1 day – work done
by C and A in 1 day

1 1 94 5
−
= − = =
16 36 144 144
144 4
Thus, B alone can complete the work in days, i.e., 28 days.
5 5

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