C worked for all the days till the work is completed. b works for first 12 days and then left and after 3 days d joined c and they eorked till work completed.a work for last 20 days. each man did equal share of work. if a and c together can complete the work in 48 days. then in how many days a ,b,d together can complete the work..?
Answers
Given : C worked for all the days till the work is completed. b works for first 12 days and then left and after 3 days d joined c and they eorked till work completed.a work for last 20 days. each man did equal share of work.
To find : how many days a ,b,d together can complete the work.
Solution:
Let say Work Completed in F Days
C worked for F Days
B Worked for 12 Days
D worked for F - 12 - 3 = F - 15 Days
A Work for 20 Days
Let say A , B , C & D there each day work
then Total Work = CF + 12B + D(F - 15) + 20A
also each man did equal share of work
=> CF = 12B = D(F - 15) = 20A
Total work = 4 * CF = 4 * 12B = 4D(F - 15) = 4 * 20A
12B = 20 A => A = 0.6B or B = 5A/3
a and c together can complete the work in 48 days
=> 48A + 48C = 4 * 20A
=> 48C = 32A
=> 3C = 2A
=> A = 1.5C
CF = 20A
=> CF = 20 * 1.5C
=> F = 30
=> 30C = 12B = 15D = 20A
15D = 20A
=> 3D = 4A
=> D = 4A/3
Let say A , B & D complete work in N Days
=> (A + B + D) N = 80A
=> (A + 5A/3 + 4A/3)N = 80A
=> AN(4) = 80A
=> N = 20
a ,b,d together can complete the work. in 20 Days
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