Hello Maruti Sir, Could you please tell shortcut to solve this question, Or anyone else who has any best approach.

Akshay, Manoj and Harshit are employees of XYZ firm. Akshay while working alone takes 3 hours more than twice the time taken by all three working together to complete a piece of work.…

Question

Hello Maruti Sir, Could you please tell shortcut to solve this question, Or anyone else who has any best approach.

Akshay, Manoj and Harshit are employees of XYZ firm. Akshay while working alone takes 3 hours more than twice the time taken by all three working together to complete a piece of work. To complete the same piece of work, Manoj alone takes five times the time taken by all three working together and Harshit alone takes 9 hours less than four times the time taken by all three. How long will it take for Akshay and Harshit together to complete the work?

1. 7.5 hours 
2. 8.5 hours
3. 9.5 hours 
4. 12.5 hours

Please tell shorcut to solve this question

Arnav Gandhi · Answer

Hi 
As all three employees work is given with respect to time taken by all 3 
So we will consider time taken by all 3 to be x days
so time taken by Akshay will be 2x+3 ;Manoj will be 5x and Harshit will be 4x-9 
Now as we know time taken together by all and time taken by individual 
so we will equate their 1 day work 
so we get 
1/2x+3 + 1/5x +1/4x-9 =1/x
1/2x+3 +1/5x = 1/x - 1/4x-9
(7x+3)/10x^2+15x = (3x-9)/4x^2-9x
28x^3-63x^2+12x^2-27x=30x^3+45x^2-90x^2-135x
2x^3+6x^2-108x=0
x(2x^2+6x-108)=0
2x(x^2+3x-54)=0
2x(x+18)(x-6)=0
so we get x=6 
Therefore time taken by Akshay = 15 , by Harshit = 15 
So together they will take 7.5 hours to complete the work

Dhruv Sharma · Answer

THANK YOU SO MUCH

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