2 women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery, and that taken by 1 man alone.
Answers
Given : 2 women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days.
Solution:
Let one woman finish the work in x days and 1man finish the work in y days.
work of 1 woman in 1 day = 1/x
work of 1 man in 1 day = 1/y
A.T.Q,
Case : 1
One day's work of 2 women and 5 men= 1/4
(2/x + 5/y) = 1/4
2/x + 5/y = ¼…………..(1)
Case : 2
One day's work of 3 women and 6 men= 1/3
(3/x + 6/y) = ⅓..........(2)
On Putting 1/x = p and 1/y = q in equation (1) & (2) we get
2p + 5q = ¼
4(2p + 5q) = 1
8p + 20q = 1…………….(3)
3p + 6q = ⅓
3(3p + 6q) = 1
9p + 18q = 1……………(4)
On multiplying eq 3 by 9 equation 4 by 8 and then subtracting equation 4 from equation 3,
9(8p + 20q) - 8(9p + 18q)= 9 - 8
72p + 180q -72p -144q = 1
180q - 144q = 1
36q = 1
q = 1/36
On Putting q = 1/36 in eq (4),
9p + 18q = 1
9p + 18 × 1/36 = 1
9p + ½ = 1
9p = 1 - ½
9p =( 2-1)/2
9p = ½
9p × 2 = 1
18p = 1
p = 1/18
p = 1/x = 1/18 and q = 1/y = 1/36
x = 18 and y = 36
Hence, one woman can finish the work in 18 days and 1 man can finish the work in 36 days.
Hope this answer will help you…
Some more questions from this chapter :
8 Women and 12 men can complete a work in 10 days while 6 women and 8 men can complete the same work in 14 days. Find the time taken by one woman alone and that one man alone to finish the work. What value is indicated from this action?
https://brainly.in/question/2817961
Pinky scored 40 marks in a test getting 3 marks for each right answer and losing 1 mark for each wrong answer.Had 4 marks been awarded for each correct answer and 2 marks were deducted for each wrong answer, then pinky again would have scored 40 marks. How many questions were there in the test?
https://brainly.in/question/2811091
Answer:
Step-by-step explanation:
Solution:-
Let the number of days taken by a woman and a man be x and y.
According to the question,
⇒ 4(2/x + 5/y) = 1
⇒ 2/x + 5/y = 1/4
⇒ 3(3/x + 6/y) = 1
⇒ 3/x + 6/y = 1/3
Putting 1/x = p and 1/y = q in these equations, we get
⇒ 2p + 5q = 1/4
By cross multiplication, we get
⇒ p/-20 - (-18) = q/-9 - (-18) = 1/144b- 180
⇒ p/-2 = q/-1 = 1/-36
⇒ p/-2 = - 1/36 and q/-1 = 1/-36
⇒ p = 1/18 and q = 1/36
⇒ p = 1/x = 1/18 and q = 1/y = 1/36
⇒ x = 18 and y = 36
Number of days taken by a woman = 18
Number of days taken by a man = 36