Question

Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take 8/3 more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs, 450, then in how many days did A, B and C together complete the whole work?

Answer 1

Answer:

4 Days

Step-by-step explanation:

Let say A , B & C takes A , B & C days respectively to complete the work

=> A , B & C 's 1 day work  = 1/A , 1/B & 1/C respectively

B& C complete work in  1/(1/B + 1/C)

A B & C complete work in 1/(1/A + 1/B + 1/C)

1/(1/B + 1/C)  = 1/(1/A + 1/B + 1/C)   * (3/2)

=> 2(1/A + 1/B + 1/C)  = 3(1/B + 1/C)

=> 2/A = 1/B + 1/C

1/A + 1/B + 1/C = 1/A + 2/A = 3/A

Time taken to complete work together by A , B & C = A/3

work done by B in A/3 days  =  A/3B

=> A/3B  = 120/450

=> 5A = 4B

1/(1/A + 1/B)  = A/3  + 8/3

=> 1/(1/A + 4/5A)  + A/3 + 8/3

=> 5A/9 = A/3 + 8/3

=> 5A = 3A + 24

=> 2A = 24

=> A = 12

did A, B and C together complete the whole work = A/3  = 12/3 = 4 Days

Answer 2

Answer: 4

Step-by-step explanation:

Let us Assume A,B,C take X days to complete the work;

then B and C took 50% more number of days means X+X/2= 3X/2 Days...

so The days ratio of A+B+C:B+c= X:3X/2== 2X:3x;

efficiency of these ratio is 3X:2X;

so the efficiency of A is X;(3X-2X)

so total is 450 rupees is equal to 3X in which A's Contribution is X means 450/3X*x=150 rupees;

and 120 rs is for B that means remaining 180 rupees for C;

according to this 150:120:180=5:4:6;

these r the work efficiencies of A,B,C; so Days are 1/5:1/4:1/6= 12:15:10;

all working together means (1/12+1/15+1/10)*Y=1 then Y=4 days