Question

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work alone. What are the moral values reflected in this question which are to be adopted in our life?

Answer 1

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...

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let B will take x days to complete the work.

Work done by B in 1 day = 1/x

And A will complete the work = x - 10

Work done by A in 1 day= 1/(x - 10)

According to the Question,

⇒ 1/x +  1/(x - 10) = 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, 4  (Neglecting 4)

⇒ x = 30

Hence,  the time taken by B to finish the work in 30 days.