Question

Yogesh require 3 days more than Vivek to do work. If both of them work

together, the work can be completed in 2 days. Find number of days require

by each of them to complete the work​

Answer 1

Answer:-

Let us assume that,

Vivek takes x days to the complete the work.

⟶ Amount of work completed by Vivek in x days = 1

⟶ Amount of work completed by Vivek in 1 day = 1/x.

Given that:

Yogesh requires 3 more days to complete the work.

⟶ Time taken by Yogesh = (x + 3) days.

⟶ Amount of work completed by Yogesh in (x + 3) days = 1

⟶ Amount of work completed by Yogesh in 1 day = 1/ x + 3.

Also given that,

They can complete the work together in 2 days.

⟶ Work completed by both in 2 days = 1

⟶ Work completed by both in 1 day = 1/2.

According to the question ,

⟶ (1/x) + (1/x + 3) = 1/2

⟶ (x + 3 + x) / x(x + 3) = 1/2

⟶ 2(x + 3 + x) = x² + 3x

⟶ 2x + 6 + 2x = x² + 3x

⟶ x² + 3x - 2x - 2x - 6 = 0

⟶ x² - x - 6 = 0

⟶ x² - 3x + 2x - 6 = 0

⟶ x (x - 3) + 2(x - 3) = 0

⟶ (x + 2)(x - 3) = 0

★ x + 2 = 0

x = - 2

★ x - 3 = 0

x = 3

Time cannot be negative So positive value is taken.

Therefore,

• Number of days required to Vivek to complete the work = x = 3 days.

• Number of days required to Yogesh to complete the work = x + 3 = 3 + 3 = 6 days.

Answer 2

Answer:

✰ Given :-

• Yogesh require 3 days more than Vivek to do work. If both of them work together, the work can be completed in 2 days.

✰ To Find :-

• How many days require by each of them to complete the work.

✰ Solution :-

⋆ Let, Vivek do complete the work in x days.

⋆ Then, Yogesh do complete the work in x + 3.

➣ According to the question :-

↣ $\dfrac{1}{x}$ + $\dfrac{1}{x + 3}$ = $\dfrac{1}{2}$

↣ $\dfrac{x + 3 + x}{x(x + 3)}$ = $\dfrac{1}{2}$

↣ $\dfrac{2x + 3}{x² + 3x}$ = $\dfrac{1}{2}$

↣4x + 6 = x² + 3x

↣x² + 3x - 4x - 6 = 0

↣x² - x - 6 = 0

↣x² - (3 - 2)x - 6 = 0

↣ x² - 3x + 2x - 6 = 0

↣ x(x - 3) + 2(x - 3) = 0

↣ (x - 3) (x + 2) = 0

↣ x = 3 , x = - 2

Here x = 3, - 2 but time can not be negetive.

$\therefore$ ➙ Number of days require Vivek to complete the work = x = 3 days

➙ Number of days require Yogesh to complete the work= x + 3 = 3 + 3 = 6 days.

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