Question

400 persons, working 9 hrs per day complete 1/4th of the work in 10 days. The number of additional persons, working 8 hrs per day, required to complete the remaining work in 20 days, is:

Answer 1

let number of workers completing the work in 20 days be as x

work done = 1/4

remaining work = 1- 1/4 = 3/4

hours per day 8:9

work 1/4 :3/4

days 20:10::400:x

8 x 1/4 x 20  x X=9 x 3/4 x 10 x 100

40x = 27000

x = 675

additional men = 675-400 =275

Answer 2

CONCEPT:

the concept used here is the concept of ratio.

TOTAL WORK=( no of person*hours worked*days need to  complete)/work completed or wage got.

we should equalise the ratio before and after the change in workers, hours etc and find the variable

GIVEN:

total no of persons before addition=400

time required by 400 persons to complete 1/4 th of work=9 hours.

completed work=1/4th

FIND:

Number of persons working 8 hours per day required to complete the remaining work in 20 days;

SOLUTION:

let the number of people completing the work in 20 days=x.

remaining work=3/4 th part of work.

ratio of hours per day now and then(before addition of workers and after addition of workers)=8:9

ratio of work now and then(before addition of workers and after addition of workers)=1/4:3/4

days now and then(before addition of workers and after addition of workers)=20:10

persons required now and then(before addition of workers and after addition of workers)=x:400

so in whole lets make the ratio.

8*1/4*20*x=9*3/4*10*400

40x=27000

x=675

so the  number of total workers is 675

so the number of additional workers=675-400=275

so the number of additional persons, working 8 hrs per day, required to complete the remaining work in 20 days, is 275

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