Time and Work Intuitive way

Question

I am currently practising some basic time and work questions, and focusing more on doing the stuff in an intuitive way (i.e. in the simplest way possible): I am facing a doubt regarding the way I’m thinking about the question and the way the solution is provided in textbook.

So the question is,

4 men and 6 women together do the job in 8 days, and 3 men and 7 women does the same job in 10 days.How many days the same job will be done by 10 women?

My approach is :

Considering an common multiple of 10 days and 8 days given above, i choose lets say 80, so here 80 is total unit of work. so that means in first case, 4M and 6W does job in 8 days, means they do 80/8 i.e 10 unit of work per day and similarly for second case 3M and 7W in 10 days means 80/10 i.e. 8 unit of work per day. So inorder to find how many unit of work is done by M alone and W alone, i basically simulatenously solve the equation,

$$i)\ 4M+6W=10$$ (multiply by 3).

$$ii)\ 3M+7W=8$$(multiply by 4).

Here after solving the above equation simultaneously, i get work done by W per day is 1/2 units and work done by M per day = 7/4 units. This above value when substituted in first equation it satifies but for second equation i get value as 8.75 units which is not accurate right? it should be 8. Well i know the alternate solution for the above question but want to know where i m wrong in these approach, Thanks for you kind help!:)

"So the question is, 4 men and 6 women together do the job in 8 days, and 3 men and 7 women does the same job in 10 days. looks quite simple my approach is :" I don't see a question. — John Douma, Jul 03 '22 at 16:05

score 1 · Accepted Answer · answered Jul 03 '22 at 17:12

1

You have made a calculation error: the correct answer should be $\displaystyle M=\frac{11}{5},\ W=\frac 15$.

Thus 10 women work 2 units a day and hence take 40 days to complete the assignment.

answered Jul 03 '22 at 17:12

insipidintegrator

6,642

sometimes i become so ignorant! Thankyou for this clarification! @insipidintegrator .... much appreciated!! – Niraj Jain Jul 03 '22 at 17:20
Thanks @insipidintegrator ! no friend now its alright! accepted your answer. – Niraj Jain Jul 03 '22 at 17:25

score 1 · Answer 2 · answered Jul 03 '22 at 17:26

1

I'd suggest using conceptually simpler variables, like taking per day work of men as 'm' and that of women as 'w'. Rest of my answer is the solution with these, rather than what you asked.

Writing the two given statements about total work (TW) in above assumed variables :

TW = (4m + 6w)*8 = (3m + 7w)*10

Simplifying these gives: m = 11w; and further TW = 400w. Diving TW by 10 gives you the number of days 10 women will take.

answered Jul 03 '22 at 17:26

Madhur

11

Thanks @Madhur ...i like your approach too!! :) – Niraj Jain Jul 03 '22 at 17:44

score 0 · Answer 3 · edited Jul 17 '22 at 18:51

There is a fundamental problem with this- it assumes that every man works at the same rate and every woman works at the same rate- and that is just not true!

But assuming this, let $x$ be the rate at which men work, in "jobs per day" and let y be the rate at which women work, in "jobs per day". We are told that "$4$ men and 6 women together do the job in 8 days, so 4x+ 6y= 1/8 and "and 3 men and 7 women does the same job in 10 days", so 3x+ 7y= 1/10. Solve for x and y.

Time and Work Intuitive way

3 Answers3