a person p takes 4 days less than q to finish a work if the work on alternate days starting with p it takes them 9.5 days to finish the work in how many days p alone can finish the work
Answers
Answer:
let q=t day so p=t-4day so efficiency of Pand q is t and t-4 now 5t+9/2(t-4) =t(t-4) so 19t-36=2t2-8t so 2t2-27t+36=0 for solving we get t=12, 3/2 so p time =t-4=12-4=8 day ans
Given : a person p takes 4 days less than q to finish a work
they work on alternate days starting with p it takes them 9.5 days to finish the work
To Find : in how many days p alone can finish the work
Solution:
p alone can finish the work in d days
Then q alone can finish the work in d+ 4 days
p's 1 day work = 1/d
q's 1 day work = 1/(d + 4)
they work on alternate days starting with p it takes them 9.5 days to finish the work
=> p works for 5 days and q work for 4.5 days
Work done
5 * 1/d + 4.5 * 1/ (d + 4) = 1
=> 10/d + 9/(d + 4) = 2
=> 10(d + 4) + 9d = 2d(d + 4)
=> 19d + 40 = 2d² + 8d
=> 2d² - 11d - 40 = 0
=> 2d² -16d + 5d - 40 = 0
=> 2d(d - 8) + 5(d - 8) = 0
=> (2d + 5) (d - 8) = 0
=> d = 8 as days can not be negative
Hence p alone can finish the work in 8 days
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