B and C can complete the work is 50% more time than A B&C. if they together on a job till the whole work completed than B earn Rs. 120.out of total 450, then find how much time they together complete the whole work if A&B takes 8/3 more numbers of days to complete the work than A, B&C.
Answers
Answer:
4 days
Step-by-step explanation:
If a, b, and c will take x days, then b and c take 50% more days
Thus x + x/2 = 3x/2 days
Ratio = a+b+c : b+c = x : 3x/2 = 2x : 3x
Ratio of efficiency = 3x : 2x
Efficiency of A-
(A + B + C) - (B + C) = 3x - 2x
A = x
Efficiency of A 1/3rd of (A+B+C) [ 1/3×3x = x]
Share of B = 120 out of 450 = 120/450 = 4/15
Ratio of efficiencies-
A = 1/3 = 5/15 B = 4/15 C = (15-4-5)/15 = 6/15
i.e. 5 : 4 : 6
Ratio of number of days = 1/5 : 1/4 : 1/6
= 60x/5 : 60x/4 : 60x/6
= 12x : 15x : 10x
One day work of A and B = 1/12x + 1/15x = 9/60x
Thus, A and B will take 60x/9 days to complete the work.
Therefore, A,B and C will take = 1/12x + 1/15x + 1/10x = 15/60x
So, A,B and C will take 60x/15 days to complete the work.
A and B take 8/3 days more than A, B and C (Given)
Thus, 60x/9 - 60x/15 = 8/3 = x = 1
Thus number of days A, B and C = 60x/15 = 4x = 4×1 = 4 days