12. A and B together can build a wall in 10 days; B and C working together can do it in
15 days; C and A together can do it in 12 days. How long will they take to finish the
work, working all together? Also find the number of days taken by each to do the
same work, working alone.
Answers
Answer:
Together they will do the work in 4 days
A will do the work in 11 days
B will do the work in 8 days
C will do the work in 6 days
Step-by-step explanation:
1/10+1/15+1/12
30+20+25/300
1/4
A=15-4=11
B=12-4=8
C=10-4=6
Let the total work = 1
A + B can complete work in = 10 days
Work of A and B in 1 day = 1 / 10
B + C can complete work in = 15 days
Work of B and C in 1 day = 1 / 15
A + C can complete work in = 12 days
Work of A and C in 1 day = 1 / 12 .
Total work by all in 1 day = 2 ( A + B + C ) = 1 /10 + 1/ 15 + 1/ 12 = 6 + 4+ 5 / 60 = 15 / 60 = 1 / 4 .
2 (A + B + C) = 1 / 4
A + B + C + = 1 / 4 ÷ 2 = 1 / 4 × 1/ 2 = 1/ 8
A + B + C can do 1 / 8 in 1 day
A + B + C can do 1 work in = 1 ÷ 1 / 8 = 1 × 8 /1 = 8 days . ( days required by A , B and C to complete the work if they work together )
work completed by A , B and C in 1 day = 1 / 8
Work completed by B + C in 1 day = 1 /15 .
Work done by A in 1 day = 1 / 8 - 1 / 15 = 15 - 8 / 120 = 7 / 120
days required by A to complete 1 work = 1 ÷ 7 / 120 = 120 / 7 = 17 whole 1 / 7 days .
work completed by A+ B +C = 1 / 8
Work completed by C + A in 1 day = 1 / 12
work done by B in 1 day = 1/ 8 - 1/ 12 = 3 - 2 / 24 = 1 / 24 .
Days required by B to complete 1 work = 1 ÷ 1 / 24 = 1 × 24 / 1 = 24 days
work completed by A + B + C = 1 / 8
work completed by A + B in 1 day = 1 / 10
Work done by C in 1 day = 1 / 8 - 1 / 10 = 5 - 4 / 40 = 1 / 40 .
Days required by C to complete 1 work = 1 ÷ 1 / 40 = 1 × 40 / 1 = 40 days
thus , A = 17 whole 1 / 7 days , B = 24 days , C = 40 days and A+ B + C = 8 days to complete 1 work . t