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# Tina can do as much work in 2 days as Leena can do in 3 days and Leena

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Joined: 02 Sep 2009
Posts: 62289
Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

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19 Jan 2020, 23:31
00:00

Difficulty:

75% (hard)

Question Stats:

45% (03:01) correct 55% (03:33) wrong based on 22 sessions

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Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?

A. 50 days
B. 60 days
C. 66 days
D. 72 days
E. 75 days

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Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

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20 Jan 2020, 00:53
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Question)
Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?

Solution:
Work by Tina in 2 days = Work by Leena in 3 days
Work by Leena in 4 days = Work by Meena in 5 days

Combining: Work by Tina in 8 days = Work by Leena in 12 days = Work by Meena in 15 days

Let the work be the LCM (least common multiple) of 8, 12, 15 = 120 units
=> Work by Tina in 8 days = Work by Leena in 12 days = Work by Meena in 15 days = 120 units

=> Work by Tina in 1 day = 15 units; Work by Leena in 1 day = 10 units; Work by Meena in 1 day = 8 units
=> Work done by all three together in 1 day = 33 units
=> Work done by all three together in 20 days (total work duration) = 660 units

Thus, total work volume is of 660 units
=> Time taken by Leena to complete the work = 660/10 = 66 days

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Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

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09 Feb 2020, 23:49
Bunuel wrote:
Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?

A. 50 days
B. 60 days
C. 66 days
D. 72 days
E. 75 days

Solution

• Let us assume that the time taken by Leena to finish the required work alone is x days.
• Also, let us assume that the working rate of Tina, Leena and Meena be t, l, and m units per days.
• Now, Tina can do as much work in 2 days as Leena can do in 3 days
o $$2t =3l ⟹ t = \frac{3l}{2} …………. Eq. (i)$$
• And, Leena can do as much work in 4 days as Meena can do in 5 days.
o So, $$4l =5m ⟹ m = \frac{4l}{5} …………. Eq. (ii)$$
• Now, work done by Leena in x days = work done by all three in 20 days
o $$l*x = (t + l + m) *20$$
o Substituting the values of t and m from Eq.(i) and Eq(ii) into the above equation,
 $$l*x = (\frac{3l}{2} + l + \frac{4l}{5})*20$$
 Or, $$l*x = \frac{(15l + 10l + 8l)}{10}*20$$
 Or, $$x = 66$$ days.
Thus, the correct answer is Option C.
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Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena   [#permalink] 09 Feb 2020, 23:49
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