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Question

Two people working together can finish the work in 2255 minutes. If one person takes 8 minutes more than the other person to finish it, find the second degree equation from which we can find time in which the faster person would finish the work.

A

45x2+396x176=0

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B

55x2+396x176=0

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C

55x2+386x176=0

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D

55x2+396x186=0

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Solution

The correct option is B 55x2+396x−176=0 Let the faster person take x minutes to finish the work. Therefore, the slower person will take (x+8) minutes to finish the work. ∴ The part of the work finished by the faster person in one minute =1x ⇒ The part of the work finished by the slower person in one minute =1x+8 It is given that the work is finished in 2255 minutes ⇒The part of the work finished in one minute by both the people together =5522 ⇒1x+1x+8=5522 x+8+xx(x+8)=5522 ⇒22 (2x+8)=55x (x+8) ⇒44x+176=55x2+440x ⇒55x2+396x−176=0

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