A can do 2/3 of a certain work in 16 days and B can do 1/4 of the same work in 3 days. In how many days can both finish the work, working together?
Answers
A and B can both finish the work in 8 days.
Explanation:
Given Condition:
1. A can do 2/3 of a certain work in 16 days.
2. B can do 1/4 of the same work in 3 days.
To find:
How many days can both finish the work
According to condition1,
A can do 2/3 of work in 16 days
==> So, find the A's one day work
==> 16 days = 2/3 work
==> Divide by 16 on both sides, to get one day work
==> 16 ÷16 = 2/3÷16
==> 1 = 2/3 ÷16/1
==> 1 = (2/3)×(1/16)
==> 1 = 1/(3×8)
==> 1day = 1/24 work
==> A can do 1/24 work in 1 day
According to condition2,
A can do 1/4 of work in 3 days
==> So, find the B's one day work
==> 3 days = 1/4 work
==> Divide by 3 on both sides, to get one day work
==> 3 ÷3 = 1/4÷3
==> 1 = 1/4 ÷3/1
==> 1 = (1/4)×(1/3)
==> 1 = 1/(4×3)
==> 1day = 1/12 work
==> B can do 1/12 work in 1 day
==> Add the one day work of both A and B ,to find A's and B's work
together,
==> A's one day work + B' s one day work
==> A+ B = 1/24 + 1/12
Denominator is different so, taking lcm
==> A+B = 1/24 + 1(2)/12(2)
==> A+B = 1/24 + 2/24
==> A+B = 3/24
==> A+B = 1/8
==> 1 represents's the per day work of A and B
==> 8 represent's the total work of both A and B
A and B can both finish the work in 8 days.