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# Sunil takes 5 days more than Anil to complete a certain work. 4 day after starting the work, Anil left the work. The remaining work was done by Sunil in 5 days. Find how many days each will take to complete the work.

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Solution

## Let Anil takes x number of days to complete the work⇒1 day =1x of the work.Sunil takes 5 more days than Anil to complete the work.⇒x+5 days⇒1 day =1(x+5) of the workTogether:1 day =1x+1x+51 day =(x+5+x)x(x+5)1 day =(2x+5)(x2+5x) of work doneTo find 4 days of work done:1 day =(2x+5)(x2+5x)4 days=4(2x+5)(x2+5x) 4 days =(8x+20)(x2+5x) of work doneTo find the amount of work left to be done:Work left =1−(8x+20)(x2+5x)Work left =(x2+5x−8x−20)(x2+5x)Work left =(x2−3x−20)(x2+5x)Solving for x:Give that Anil needs 5 days to complete the rest of the work(x2−3x−20)(x2+5x)×(x+5)=(x2−3x−20)x⇒5x2−3x−20=5xx²−8x−20=0(x−10)(x+2)=0∴x=10 or x=−2 (Rejected, number of days cannot be negative)To find the number of days each take to complete the workAnil =x=10 daysSunil =x+5=10+5=15 daysThus, Anil takes 10 days and Sunil takes 15 days to complete the work.  Suggest Corrections  0      Similar questions  Related Videos   Time and Work
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