sunil takea 5 days more than anil to complete a work. 4 days after starting a work anil left the work. the remaining work done by sunil in 5 days . find how many day each one will take to complete the work
Answers
Let Anil takes x number of days to complete the work
⇒ 1 day = 1/x of the work
Sunil takes 5 more days than Anil to complete the work
⇒ x + 5 days
⇒ 1 day = 1/(x + 5) of the work
Together:
1 day = 1/x + 1/(x + 5)
1 day = (x + 5 + x)/x(x+5)
1 day = (2x + 5) / (x² + 5x) of work done
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 done
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)
Solve x:
Give that Anil needs 5 days to complete the rest of the work
(x² - 3x - 20) / (x² + 5x) ÷ 1/(x + 5) = 5
(x² - 3x - 20) / (x² + 5x) × (x + 5) = 5
(x² - 3x - 20) /x = 5
x² - 3x - 20 = 5x
x² - 8x - 20 = 0
(x - 10) (x + 2) = 0
x = 10 or x = -2 (Rejected, number of days cannot be negative)
Find the number of days each take to complete the work
Anil = x = 10 days
Sunil = x + 5 = 10 + 5 = 15 days
Answer: Anil takes 10 days and Sunil takes 15 days to complete the work.
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