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Mrunal is thrice as efficient as Hina. Mrunal started the work and worked for 6 days after which she was replaced by Hina. Hina worked for 9 more days. After that they completed rest of the 50% work together. How many days will Hina take alone to complete the work?

Mrunal is thrice as efficient as Hina. Mrunal started the work and worked for 6 days after which she was replaced by Hina. Hina worked for 9 more days. After that they completed rest of the 50% work together. How many days will Hina take alone to complete the work? Correct Answer 54

Let number of days taken alone by Mrunal be x and by Hina be y.

Since, Mrunal is thrice as efficient as Hina. Time taken by Hina to complete the work will be three times that of Mrunal to complete the same work.

⇒ y = 3x

Work done by Mrunal in 1 day = 1/x

Work done by Hina in 1 day = 1/y = 1/3x

Mrunal works for 6 days and then, Hina works for another 9 days and complete 50% of the work.

⇒ 6/x + 9/3x = 50/100

⇒ 27/3x = 0.5

⇒ x = 9/0.5 = 18

Thus, Mrunal alone takes 18 days to complete the work.

∴ Time taken by Hina = 3 × 18 = 54 days

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