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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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Math Expert
Joined: 02 Sep 2009
Posts: 64111
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
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Difficulty:

45% (medium)

Question Stats:

65% (02:55) correct 35% (03:33) wrong based on 34 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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Joined: 11 Aug 2017
Posts: 5
Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena  [#permalink]

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22 May 2020, 23:53
1
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 :
The question is asking us to identify the number of days Leena would take in case she is working alone :
All 3 people working together takes - 20 days
When Leena is working alone, she will have to finish the work completed by her as well as the work completed by the other two. So, total number of days Leena will take
= 20 + Number of days Leena take to finish Meena's Work + Number of days Leena take to finish Tina's Work
= 20 + (20*4/5) + (20*3/2)
= 20 + 16 + 30
= 66 days
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Joined: 07 May 2019
Posts: 697
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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]

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23 May 2020, 02:01
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

Lets Tina can do work in 2 days =x units
Tina's Per Day Rate = x/2

Leena can do work in 3 days = x units
Leena's per day rate = x/3

Leena can do work in 4 days = 4x/3 = Meena can do work in 5 days

Meena's per day rate = 4x/15

Total work done in 20 days = $$20*(x/2+x/3+4x/15)$$

Solving this, we get 22x

If Leena has to do same work, $$22x/x/3$$= 66 days

Re: Tina can do as much work in 2 days as Leena can do in 3 days and Leena   [#permalink] 23 May 2020, 02:01