A can do a piece of work in 20 days while B can do it in 30 days. They work together for 10 days and the rest of the work is done by C in 5 days. If they get Rs 560 for the whole work, how much money will A get?

Question

Question

Answer 1

Given:

Time is taken by A to do the work = 20 days

Time is taken by B to do the work = 30 days

Total wage = Rs. 560

Formula used:

Time = Total work/Efficiency

Concept used:

Wage is divided the same as efficiency and inversely proportional to the time taken

Calculation:

Work done by A in 1 day is = 1/20

Work done by B in 1 day is = 1/30

Work done by A and B together in 1 day is = (1/20 + 1/30) = 1/12

Work is done by A and B together in 10 days is = 10/12

Remaining work = 1 – 10/12 = 2/12 = 1/6

C do 1/6 of the work in 5 days

Total work done by C alone in 5 × 6 is = 30 days

Wages ratio of A, B and C = 1/20 × 10 : 1/30 × 10 : 1/30 × 5 = 6 : 4 : 2

Money A will get = 6/12 × 560 = 280

∴ Share of money A will get is Rs 280

Shortcut Trick

Since A can do that piece of work in 20 days and has worked for 10 days

i.e. A has done half of total work.

So A will get half of the amount paid to all i.e. = 560/2 = Rs. 280

Confusion Points

You may think that 240 is the correct answer but it is not.

It is so because the time for which C has worked is 5 days whereas A and B have worked for 10 days.

Thus, Wages ratio of A, B and C = 1/20 × 10 : 1/30 × 10 : 1/30 × 5 = 6 : 4 : 2