Math, asked by Rimmyy6783, 11 months ago

B is 20% more efficient than a. B started the work & did it for x days. And then b is replaced by a. A completed the remaining work in x+8 days. Ratio of work done by a & b is 2:3. In how many days a & b working together can complete the whole work?

Answers

Answered by amitnrw
0

Given :  B is 20% more efficient than A  

B started the work & did it for x days.

And then b is replaced by a.  A completed the remaining work in x+8 days.

Ratio of work done by A & B is 2:3.

To Find :  In how many days A & B working together can complete the whole work

Solution:

A' s 1 day work   =   k

B is 20% more efficient than A  

=> B's 1 day work  = k + (20/100)k = 1.2k

Work done by  B in x days  =  1.2kx

Work done by  A in x+8  days  =  k ( x + 8)

Ratio of work done by A & B  is 2 : 3

=>   k ( x + 8) /   1.2kx    = 2 /3  

=>   3x  + 24  = 2.4x

=> 0.6x  = 24

=> x  =  - 40

Hence mistake in data

Assuming Ratio of work done by A & B  is 3 : 2

=>   k ( x + 8) /   1.2kx    = 3/2

=> 2x + 16  = 3.6x

=> 1.6x = 16

=> x = 10

Work done by  B in x days  =  1.2*k *10  =   12k

Work done by  A in x+8  days  =  k ( 10 + 8) = 18k

Total Work = 12k + 18k = 30k

Total work in 1 day = k + 1.2k  = 2.2k

Time taken =  30k/2.2k  = 13.63  

A &  B working together can complete the whole work in   13.63   days

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