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A and B complete a work in 2 days. If A alone can do it in 38 days, then B alone can do 9 times of the same work in ______________ days.
Question

A and B complete a work in 2 days. If A alone can do it in 38 days, then B alone can do 9 times of the same work in ______________ days.

A.

10

B.

9

C.

20

D.

19

Correct option is D

Given:

A and B together complete the work in 2 days.

A alone can complete the work in 38 days.

Solution:

Total work = LCM of ( 2, 38) = 38

Efficiency of A  + B = 382=19\frac{38}{2} = 19  unit per day 

Efficiency of A =  3838\frac{38}{38} = 1 unit per day 
Efficiency of B = 19 - 1 = 18 unit per day

9 times of the work = 9×38\times 38  

B alone complete the work = 9×3818=19\frac{9×38 }{18} = 19  days

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