Problems on Work and Wages

Problems on Work and Wages with explanation

Q. A can do a piece of work in 3 days while B can do the same work in 4 days. If they work together for a total wages of 2800, how much does A get? [Bank Clerks 2009]
Solution
A's 1 day's work = 1/ 3
B's 1 day's work = 1 /4
A's share : B's share
   = 1 / 3 : 1 / 4
   = 4 : 3
A's share = 4/7 × 2800
                = 1600

Q. A alone can do a piece of work in 3 days, while B alone can do the same work in 2 days. If they work together to complete the work, their total wages is fixed 225. Find the share of A. [RRB 2008]
Solution
A's 1 day's work = 1 / 3
B's 1 day's work = 1 / 2
A's share : B's share = 1 / 3 : 1 / 2
                                 = 2 : 3
Share of A = 2 / 5 × 225
                  = 90


Q. A alone can finish a work in 2 days, while B alone can finish it in 3 days. If they work together to finish it, then out of total wages of 6000, what will be the 20% of A's share? [Hotel Mgmt. 2009]
Solution
A's 1 day's work = 1/ 2
B's 1 day's work = 1 /2
A's share :B's share = 1 / 2 : 1 / 3
                       = 3 : 2
Therefore
A's share = (3 / 5) × 6000
                = 3600
Therefore 20% of A's share = 3600 × 20 / 100
                                    = 720
Q. Vandana can do a piece of work in 10 days. With the help of Ruchi, she can do the same work in 6 days. If they get 200 for that work, then what will be the share of Ruchi in the received remuneration?
Solution
Vandana's 1 day work = 1/10
( Vandana + Ruchi)'s 1 day's work = 1 / 6
Therefore Ruchi' s 1 day's work = 1/ 6 - 1/10
                                 = 4/60 = 1/15
Ratio of wages of Vandana and Ruchi
                     = 15 : 10
Ruchi's wages ={A /( A + B)} × total wages
                        = (10 / 25) × 200
                        = 80

Q. A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for [SSC CCL 2013]
Solution
A's 1 day's work = 1 / 21
B's 1 day's work = 1 / 28
Therefore same money is sufficient to pay the wages of both for = 1 / { (1/21) + (1/28)}
     = (21 × 28)/ 49
     = 3× 4
     = 12 days

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