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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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