8 Q and 12 men can together finish a work in 10days while 6 women and 8 men can finish it in 14 days find the time taken by 1 women alone to finish the work and also that taken by 1 men alone
Answers
Step-by-step explanation:
Let
1 woman finish the work in X days
1 man finish the work in Y days
Now,
Work done by 1 woman in 1 day = 1 / X
Work done by 1 man in 1 day = 1 / Y
1st Part :-
8 women and 12 men finish work in 10 days ( Given )
1 day work of 8 women and 12 men = 1 / 10 of total work
Now,
8 / X + 12 / Y = 1 / 10
4 ( 2 / X + 3 / Y ) = 1 / 10
2 / X + 3 / Y = 1 / 40
2nd Part :-
6 women and 8 men finish work in 14 days ( Given )
1 day work of 6 women and 8 men = 1 / 14 of total work
Now,
6 / X + 8 / Y = 1 / 14
2 (3 / X + 4 / Y ) = 1 / 14
3 / X + 4 / Y = 1 / 28
Now,
Putting 1 / X = p and 1 / Y = q in Part 1st & 2nd
2p + 3q = 1 / 40 ( 1 )
3p + 4q = 1 / 28 ( 2 )
Multiply equation 1 by 2 and equation 2 by 1
8p + 12q = 4 / 40
8p +12q = 1 / 10 ( 3 )
9p + 12q = 3 / 28 ( 4 )
On subtracting equation 3 and 4
8p +12q = 1/10
9p + 12q = 3/28
Calculation :-
- p = 1 / 10 - 3 / 28
-p = ( 14 - 15 ) / 140
-p = -1 / 140
p = 1 / 140
Now,
Substituting p= 1 / 140 in equation 3
8p +12q = 1 / 10
8 ( 1 / 140 ) +12q = 1 / 10
8 / 140 + 12q = 1 / 10
12q = 1 / 10 - 2 / 35
12q = ( 7 - 4 ) / 70
12q = 3 / 70
q = 3 / ( 70 × 12 )
q = 1 / ( 70 × 4 )
q = 1 / 280
Now,
p = 1 / 140 = 1 / X
So, Y = 140
q = 1 / 280 = 1 / Y
Y = 280
Therefore, The time taken by
1 woman alone to finish the work = 140 days
1 man alone to finish the work = 280 days