sunil takes 5 days more than anil to complte a certain work 4 days after starting work anil left work work the remaining work was done by sunilin 5days find how many days each will take to complete work
Answers
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Answer:
Anil takes 10 days and Sunil takes 15 days
Step-by-step explanation:
Let the number of days Anil needed to complete the work be x
⇒ 1 day = 1/x
Sunil takes 5 days more than Anil to complete the work
⇒ Number of days = x + 5
⇒ 1 day = 1/(x + 5)
Find the amount of work they did in 4 days:
1 day = 1/x + 1/(x + 5)
1 day = (x + 5 + x)/x(x+ 5)
1 day = (2x + 5)/x(x+ 5)
4 days = 4(2x + 5)/x(x+ 5)
Find the amount of work Sunil did in 5 days:
1 day = 1/x + 5)
5 days = 5/(x + 5)
Solve x:
4(2x + 5)/x(x+ 5) + 5/(x + 5) = 1
4(2x + 5) + 5x = x(x + 5)
8x + 20 + 5x = x² + 5x
x² - 8x - 20 = 0
(x - 10)(x + 2) = 0
x = 10 or x = -2 (Negative, rejected)
Find the number of days each take:
Anil = x = 10 days
Sunil = x + 5 = 10 + 5 = 15 days
Answer: Anil takes 10 days and Sunil takes 15 days