Question

B and C do work together and they taking 3/2 more time than A,B,and c work together. B earn 120 rupees out of 450 rs.If B do work 8/3 days more than A,B,C work together then all work together how many time take

Answer 1

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