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
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Answer:
Number of days required by Vivek = 3 days and
Number of days required by Yogesh = 6 days
Step-by-step explanation:
Let us suppose Vivek completes the work in ' x ' number of days
So,
Viveᵈᵃʸˢ 1 day work = \frac{1}{x}x1
Yogesh requires 3 days more than Vivek to do a work completely
So,
Yogesh completes the work in ' x + 3 ' days'
Yogesh's 1 day work = \frac{1}{x+3}x+31
When they are working together, work is completed in 2 days
Therefore,
\frac{1}{x}x1 + \frac{1}{x+3}x+31 = \frac{1}{2}21
\frac{x+3+x}{x(x+3)}x(x+3)x+3+x = \frac{1}{2}21
\frac{2x+3}{x^{2}+3x}x2+3x2x+3 = \frac{1}{2}21
4x + 6 = x² +
x² + 3x - 4x - 6 = 0
x² - x - 6 = 0
Solving for x:
x² - 3x + 2x - 6 = 0
x ( x - 3 ) + 2 ( x - 3) = 0
( x + 2 ) ( x - 3 ) = 0
x = - 2 or x = 3
Since, Number of days cannot be negative
x = 3
That is,
Vivek completes the work in 3 days
And Yogesh completes the work in x + 3 days = 3 + 3 = 6 days
Hence,
Number of days required by Vivek = 3 days and
Number of days required by Yogesh = 6 ᵈᵃʸˢ
ᴵ ᵗʰⁱⁿᵏ ᵗʰⁱˢ ⁱˢ ʸᵒᵘʳ ᵃⁿˢʷᵉʳ..
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