Two workers Praveen and Mahesh are engaged to do a work. Praveen working alone takes 8 hours more to complete the job than if both worked together. If Mahesh worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?
Solution: Let Praveen and Mahesh together take x hours to complete the work. Then,
Praveen alone takes (x+8) hours and Mahesh alone takes (x+9/2) hrs to complete the work. Then,
1/(x+8) + 1/(x+9/2) = 1/x => 1/(x+8) + 2/(2x+9) = 1/x => x(4x+25) = (x+8)(2x+9)
=> 2x^2 = 72
=> x^2 =36
=> x = 6.
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