Yogesh required 3 days more than Vivek to do work completely. if both of them work together the work can be completed in 2 days. find the number of days required for each of them to do the work completely.
Answers
Answer:
Vivek = 3 days
Yogesh = 6 days
Step-by-step explanation:
Define x:
Let x be the number of days Vivek needed to complete the work
1 day = 1/x of the work
Yogesh needed 3 days more than Vivek
Yogesh = x + 3
1 day = 1/(x + 3) of the work
Find the number of days needed if they work together:
1 day = 1/x + 1/(x + 3)
1 day = (x + 3 + x)/x(x + 3)
1 day = (2x + 3)/(x² + 3x)
Number of days = (x² + 3x)/(2x + 3)
Solve x:
They need 2 days if they worked together:
(x² + 3x)/(2x + 3) = 2
(x² + 3x) = 2(2x + 3)
x² + 3x = 4x + 6
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 or x = - 2(rejected, since it cant be negative(
Find the numbers of days required by each of them:
Vivek = x = 3 days
Yogesh = x + 3 = 3 + 3 = 6 days
Answer: Vivek will need 3 days and Yogesh will need 6 days
Answer:
6, 3
Step-by-step explanation:
Hi,
Let 'x' be the number of days Vivek takes to do the work
=> In 1 day, Vivek does 1/x th of work.
Given that Yogesh requires 3 days more than vivek to do the work,
=> Number of days Yogesh takes to complete the work are 'x + 3'
=> In 1 day, Yogesh does 1/(x+3) th of work.
In 1 day, both Vivek and Yogesh does 1/x + 1/(x+3) part of work
Given that they complete the work in 2 days
=> 2(1/x + 1/(x+3) = 1
=> 2(2x + 3) = x(x+3)
=> 4x + 6 = x² + 3x
=> x² -x - 6 = 0
=> x = 3 or x = -2
Since x cannot be negative, hence x = 3
Thus Yogesh require 6 days and Vivek requires 3 days.
Hope, it helped !