2 women and 6 men together complete one embroidery in 4 days. 3 women and 6 men complete the same task in 3 days. So how long does it take for a woman to complete work independently and a man independently?
Answers
Answer:
Step-by-step explanation:
a similar question is there in NCERT
A woman's one day work = 1/x
and a man's one day work = 1/y
2/x + 5/y = 1/4 and
3/x + 6/y = 1/3
Let 1/x = a and 1/y = b
Now, 2a + 5b = 1/4 _(1)
and 3a + 6b = 1/3 _(2)
Multiplying _(1) by 3 and _(2) by 2 and subtracting
6a + 15b = 1/4
6a + 18b = 1/3
___________
0 + 3b = 1/4 - 1/3
=> 3b = 1/12
=> b = 1/(12×3)
=> b = 1/36
Putting b = 1/36 in _(1)
2a + 5(1/36) = 1/4
=> 72a + 5 = 36/4
=> 72a + 5 = 9
=> 72a = 9 - 5
=> 72a = 4
=> a = 4/72
=> a = 1/18
Now, a = 1/x = 1/18
=> x = 18
And, b = 1/y = 1/36
=> y = 36
So, 1 woman can finish the embroidery work in 18 days and 1 man can finish the work in 36 days.
Answer:-
no. of days of women = 18 days
no. of days of man = 36 days
Step by Step explanation:-
Let 1 woman can finish the embroidery work in 'x' days and 1 man can finish it in 'y' days.
A woman's one day work = 1/x
and a man's one day work = 1/y
A.T.Q.
2/x + 5/y = 1/4 and
3/x + 6/y = 1/3
Let 1/x = a and 1/y = b
Now, 2a + 5b = 1/4 _(1)
and 3a + 6b = 1/3 _(2)
Multiplying _(1) by 3 and _(2) by 2 and subtracting
6a + 15b = 1/4
6a + 18b = 1/3
___________
0 + 3b = 1/4 - 1/3
= 3b = 1/12
= b = 1/(12×3)
= b = 1/36
Putting b = 1/36 in _(1)
2a + 5(1/36) = 1/4
= 72a + 5 = 36/4
= 72a + 5 = 9
= 72a = 9 - 5
= 72a = 4
= a = 4/72
= a = 1/18
Now, a = 1/x = 1/18
= x = 18
And, b = 1/y = 1/36
=> y = 36
So, 1 woman can finish the embroidery work in 18 days and 1 man can finish the work in 36 days