[Please Solve in Detail] Four persons started to do a work together. 'A' works only in starting two days after that B, C and D works alternately starting from B. Ratio of time taken by A, B, C and Dif they work alone is 4: 3: 2: 5. If the work is completed in 12 days then in how many days A and Ccan complete the work if they work together? (a) 6 days (b) 12 days (c) 10 days (d) 8 days (e) 4 days
Answers
Given: Four persons started to do a work together, 'A' works only in starting two days, B, C and D works alternately starting from B, time taken by A, B, C and D, if they work alone is 4: 3: 2: 5, work is completed in 12 days.
To find: How many days A and C can complete the work if they work together.
Solution:
- As we know that B worked for 4 days, C worked for 3 days, D worked for three days,
So, the total days work done by a A is 2 days.
Similarly, the total days work done by a B is 4+2= 6 days.
Similarly, the total days work done by a C is 3+2= 5 days.
Similarly, the total days work done by a D is 3+2= 5 days.
- Now we have given the ratio of the time they have worked.
- So, let the common ratio be x.
- So their alone time of work to complete is 4x, 3x, 2x, 5x.
- So now :
2/2x + 6/3x + 5/2x + 5/5x = 1.
by solving this, we get:
x = 360/60 = 6
Answer:
So, the total days work done by a A is 4(6) = 24 days, B is 3(6) = 18 days, C is 2(6) = 12 days and D is 5(6) = 30 days.