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Fatima can alone prepare a assignment in x days, while Manish alone takes 5 more days than Fatima. Together they earned Rs. 1300 and completed the job in 2 days which is two days earlier than Fatima. Find the share of Fatima?

Fatima can alone prepare a assignment in x days, while Manish alone takes 5 more days than Fatima. Together they earned Rs. 1300 and completed the job in 2 days which is two days earlier than Fatima. Find the share of Fatima? Correct Answer 900

Given that alone Fatima can do a job in x days while together Fatima and Manish can do it in 2 days

Manish alone takes 5 more days than Fatima,

⇒ Manish alone time = x + 5

Together they completed the job in 2 days that is 2 days earlier than Fatima,

⇒ Fatima alone time = 4 days

⇒ Manish alone time = 4 + 5 = 9 days

∵ (Number of days worked/alone time) = Part of work done

Fatima's 2 day's work = 2/4 = 1/2 (Since, work is finished in 2 days)

Manish's 2 day's work = 2/9

∵ Total wages distribution to each person are in proportion to the work done by each person

So, 1300 is to be divided in the proportion of (1/2) : (2/9) or 9 : 4

∴ Share of Fatima = (9/13) ×1300 = Rs. 900

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