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madan taur

· started a discussion

· 1 Months ago

120 (Question:87677.0)

what should be 120

Question:
A and B can do a piece of work in 30 and 40 days respectively. They began the work together, but A left after some days and B finished the remaining work in 12 days. After how many days did A leave?
Options:
A) 18 days
B) 10 days
C) 20 days
D) 12 days
E) None of these
Solution:

Ans: (d)

By direct formula 

Req. no. of days = \(\cfrac{30\times40}{30+40}\)  \(\left [ \cfrac{40-12}{40} \right ]\)  = 12 days

Alternate Solution:

A & B 1 day work = 


\(\Rightarrow \cfrac{120}{7}\)

Work done by B in 12 day = 1 = \(\cfrac{3}{10}\)

Remaining work = 1 =  \(\cfrac{8}{10}\) = \(\cfrac{7}{10}\)

Now, \(\cfrac{7}{10}\) work was done by (A+B) in 1 day. 

= 12 day

therefore, A left in 12 day.

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