Question

If 15 men completes a work in 27 days and same work 13 women completes in 30 days. then if they work combine but after 3 days of starting one man left the work, next day one woman left the work again next day one man left the work and so on. so how many days will it be taken to complete this work?

Answer 1

Answer:

10 days approx

Step-by-step explanation:

Given ,

15 Men complete work in 27 days,

13 Women complete same work in 30 days.

Now,

consider that work is = X = 100;

We will calculate how much work 1 Men and 1 Women is doing in 1 day.

so 1 Men will do x work in 1 day is

x1 = (X/27)/15

x1=(100/27)/15

x1=0.2469       ...(1)

likewise for woman,

x2= (X/30)/13

x2=(100/30)/13

x2=0.2564          ...(2)

If they combine there work together then 1 Men and 1 Women will do work

is x3=[(X/27)/15] + [(X/30)/13]

x3=0.2469 +0.2564

x3=0.5033             ...(3)

Now, they work together continually only for 3 days, with 15 Men and 13 Women

So, work done in 3 days is

=[ (x1 * 15) + (x2*30)] * 3                           ..... by (1) and (2)

=[ (0.2469 * 15) + (0.2564 * 30) ] * 3

=[11.1486] *3                                           ...(4)

=34.1865                                                  ... (5)

Now , On day 4 one men left,

So work done on day 4 is

=11.3955 - 0.2469                          ... by (4)

=11.1486 + 34.1865                           ...by (5)

=45.3351

Now day 5 ,

=45.3351 + [ 11.1486 - 0.5033]

=45.3351 +[10.6453]

=55.9804

Now day 6,

=55.9804 +[10.6453 - 0.2469 ]

= 55.9804 + 10.3984

=66.3788

Now day 7,

= 66.3788 + [10.3981 - 0.2564]

= 66.3788 +[10.1417]

= 76.5205

Now day 8,

= 76.5205 + [10.1417 - 0.2469]

= 76.5205 + [9.8948]

= 86.4153

Now day 9,

= 86.4153 + [9.8948 - 0.2564]

= 86.4153 + [9.6384]

= 96.0537

Now day 10

= 96.0537 + [9.6384 - 0.2469]

= 105

So combine they will take approx 10 days to complete the task.