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Option 4 : 20 days

Let the work done by Kate in 1 day = x

∴ Work done by Ann in 1 day = 2x

Time taken by Kate to complete the work = 1/x

Time taken by Ann = (1/x) - 30

⇒ (1/x) - 30 = 1/2x

⇒ (1/x) - (1/2x) = 30

⇒ 1/2 = 30x

⇒ x = 1/60

∴ Time taken by them to finish the work together = 1/(x + 2x)

= 1/(1/60 + 1/30)

= 20 days
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