A is twice efficient as b. A and b together do the same work in as much time as c and d can do together. If the ratio of the number of alone working days of c to d is 2:3 and if b worked 16 days more than c then no of days which a worked alone?
Answers
Answer:
A complete Work alone in 18 Days
Step-by-step explanation:
A is twice efficient as b. A and b together do the same work in as much time as c and d can do together. If the ratio of the number of alone working days of c to d is 2:3 and if b worked 16 days more than c then no of days which a worked alone?
C completed work in 2c Days
then D complete work in 3c Days
Together C&D complete Work 1/(1/2c + 1/3c) = 6c/5 = 1.2c
A completed work in a Days
B completed work in 2a days ( as A is twice efficient)
=> Together A&B complete Work = 1/(1/a + 1/2a) = 2a/3
2a/3 = 1.2c
=> a = 1.8c
=> b = 2a = 3.6c
3.6c = 2c + 16
=> 1.6c = 16
=> c = 10
a = 1.8c = 18
A complete Work alone in 18 Days
Verification :
A - 18 Days B = 36 Days
A + B = 1/(1/18 + 1/36) = 36/3 = 12
C = 20 D = 30
C + D = 1/(1/20 + 1/30) = 60/5 = 12
36 = 20 + 16 (B = C + 16)