Abhishek and Abhinandan together can complete a work in 20 days. Abhinandan started to work alone and
completes 2/3 work and remaining work is completed by Abhishek alone. They completed the work in total
39 days. Find in how many days Abhinandan alone can complete the work it he works for whole numberof
days
Answers
Answer:
Abhinandan alone can complete the work in 36 Days
Step-by-step explanation:
Let say Abhinandan alone can complete work in A days
Work done by Abhinandan in 1 day = 1/A
Abhishek and Abhinandan together can complete a work in 20 days.
Abhishek and Abhinandan together can do work in 1 day = 1/20
Work done by abhishek in 1 day = 1/20 - 1/A = (A -20)/20A
Let say Anhinandan work for D days
then abhishek work for 39 - D days
Work done by abhinandan = D/A
work done by abhishek = (39-D)*(A -20)/20A
D/A = 2/3 => D = 2A/3
(39-D)*(A -20)/20A = 1/3
=> 3(39 - D)(A -20) = 20A
using D = 2A/3
=> 3(39 - 2A/3)(A -20) = 20A
=> (117 - 2A)(A - 20) = 20A
=> -2A² + 117A + 40A - 2340 = 20A
=> -2A² + 137A - 2340 = 0
=> 2A² - 137A + 2340 = 0
=> 2A² - 72A -65A + 2340 = 0
=> 2A(A - 36) -65(A - 36) = 0
=> (2A -65)(A -36) = 0
=> A = 65/2 A = 36
Taking only whole number answer
Abhinandan alone can complete the work in 36 Days