1. Rafiq can do a work in 10 days and Shafiq can do that in 15 days. In how many days do they together finish the work ?
2. A can do a work in p days and B can do it in 2p days. They started to do the work together and after some days A left the work unfinished. B completed the rest of the work in r days. In how many days was the work finished ?
3. 10 persons can do a work in 7 days by working 6 hours. Working how many hours per day can 14 persons finish the work in 6 days ?
1. Answer :
Let "d" be the number days taken by together to finish the work.
Rafiq is taking 10 days to complete the work and Shafiq is taking 15 days.
Work done by Rafiq in 1 day = 1/10
Work done by Shafiq in 1 day = 1/15
Part of work done by Rafiq in d days = d/10
Part of work done by Shafiq in d days = d/15
Part of work finished by both in d day = d/10 + d/15
In d days they are finishing the work :
d/10 + d/15 = 1
5d/30 = 1
5d = 30
d = 6
So, they will take 6 days to complete the work.
2. Answer :
Time taken by A = p days
A's one day work = 1/p
Time taken by B = 2p days
B's one day work = 1/2p
Let x be the number of days they work together.
Work done in x days = x(1/p + 1/2p)
= x(3/2p)
Unfinished work = 1 - (3x/2p)
To finish the remaining work, B is taking r days.
work finished in r days = r (1/1-(3x/2p))
= r(2p/2p-3x)
r(2p/2p-3x) = 2p
r = 2p-3x
3x = 2p-r
x = (2p-r)/3
Number of days taken to complete the work = x + r
= (2p-r)/3 + r
= (2p+2r)/3
= (2/3)(p+r)
3. Answer :
By comparing persons and hours,
if number of persons increased then hours taken will reduce. So, it comes under inverse proportion.
By comparing days and hours,
if the days increased then hours taken will reduce. So, it also comes under inverse proportion.
10 ⋅ 6 = 14 ⋅ x and 7 ⋅ 6 = 6 ⋅ x
So,
10 ⋅ 6 ⋅ 7 = 14 ⋅ x ⋅ 6
x = (10 ⋅ 6 ⋅ 7) / (14 ⋅ 6)
x = (10 ⋅ 6 ⋅ 7) / (14 ⋅ 6)
x = 5 h
Therefore, the required number of hours is 5 hours.
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