A takes 10 days less than B to complete a work, and together they do it in 12 days. In how
many days can B alone do the work?
Answers
Answer:
30 days
Step-by-step explanation:
Let's B alone take x days to finish the work.
B’s 1 days work = 1/x
A alone can finish the work in = x - 10
A’s 1 days work= 1/(x-10)
Given: A and B together can finish the same work in 12 days.
(A and B)'s 1 days work = 1/12
A’s 1 days work + B’s 1 days work = 1/x + 1/(x-10)
ATQ
1/x + 1/(x-10) = 1/12
(x-10) + x / x(x-10) = 1/12
x-10 + x / x² -10x = 1/12
2x -10 / x² -10x = 1/12
12(2x -10) = x² -10x
24x -120 = x² -10x
x² -10x -24x +120= 0
x² -34x +120= 0
x² 30x -4x +120= 0
x( x -30) -4(x -30)= 0
(x-30)(x-4)= 0
(x-30) = 0 or (x-4)= 0
x = 30 or x= 4
The value of x cannot be less than 10, so x= 30
Hence, the time taken by B to finish the work in 30 days.
The moral values reflected in this question which are to be adopted in our life is UNITY.
HOPE THIS WILL HELP YOU...