Question

8 men and 12 women can do a
piece of work in 10 days while
6 men and 8 women can do
the same work in 14 days find
the time taken by a single
man and single woman to do
the same work.​

Answer 1

Let 1 woman finish the work in x days and 1 man finish the work in y days.
work done by 1 woman in 1 day = 1/x
work done by 1 man in 1 day = 1/y
ATQ
Case 1:
8 women and 12 men finish work in 10 days
1 day’s work of 8 women and 12 men= 1/10 part of  work.
8/x + 12/y = 1/10
4(2/x + 3/y) = 1/10
2/x + 3/y = 1/40……….(1)
Case 2.
6 women and 8 men finish work in 14 days
1 day’s work of 6 women and 8 men= 1/14 part of  work.
6/x + 8/y = 1/14
2(3/x + 4/y) = 1/14
3/x + 4/y = 1/28……….(2)
Putting 1/x = p and 1/y = q in equations,1 & 2 ,
2p + 3q = 1/40………….(3)
3p + 4q = 1/28………….(4)
Multiply equation 3 by 4 and equation 4 by 3,
8p + 12q = 4/40
8p +12q = 1/10…………..(5)
9p + 12q = 3/28………….(6)
On subtracting equation 5 and 6,
8p +12q = 1/10
9p + 12q = 3/28
(-)   (-)      (-)
-----------------
- p = 1/10-3/28
-p = (14 - 15)/140
-p = -1/140
p = 1/140
On substituting p= 1/140 in equation 5,
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
x = 140
q= 1/280= 1/y
y = 280
Hence, the  time  taken  by one  woman alone to finish the work = 140 days and  one man alone to finish the work = 280 days.
HOPE THIS WILL HELP YOU.

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