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2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.?
Most Upvoted Answer
2 women and 5 men can together finish an embroidery work in 4 days, wh...
**Given Information:**
- 2 women and 5 men can finish the embroidery work in 4 days.
- 3 women and 6 men can finish the embroidery work in 3 days.
**Let's assume:**
- Let the work done by 1 woman in 1 day = x.
- Let the work done by 1 man in 1 day = y.
**Calculating the work done:**
- From the given information, we can determine the following equations:
- (2x + 5y) * 4 = 1 (work done by 2 women and 5 men in 4 days).
- (3x + 6y) * 3 = 1 (work done by 3 women and 6 men in 3 days).
**Solving the equations:**
- Simplifying the equations:
- 8x + 20y = 1
- 9x + 18y = 1
- Multiplying the second equation by 2 to make the coefficients of x equal:
- 18x + 36y = 2
- Subtracting the first equation from the second equation:
- (18x + 36y) - (8x + 20y) = 2 - 1
- 10x + 16y = 1
- Simplifying the equation:
- 5x + 8y = 0.5
- Multiplying the equation by 2 to eliminate the decimals:
- 10x + 16y = 1
- Solving the equations:
- 10x + 16y = 1
- 9x + 18y = 1
- Subtracting the second equation from the first equation:
- (10x + 16y) - (9x + 18y) = 1 - 1
- x - 2y = 0
- Solving for x:
- x = 2y
- Substituting the value of x in the equation 5x + 8y = 0.5:
- 5(2y) + 8y = 0.5
- 10y + 8y = 0.5
- 18y = 0.5
- y = 0.5/18
- y = 1/36
**Calculating the time taken by 1 woman alone:**
- Substituting the value of y in the equation x = 2y:
- x = 2(1/36)
- x = 1/18
- Therefore, 1 woman alone can finish the embroidery work in 1/18 days.
**Calculating the time taken by 1 man alone:**
- Since y = 1/36, 1 man alone can finish the embroidery work in 1/(1/36) = 36 days.
- 2 women and 5 men can finish the embroidery work in 4 days.
- 3 women and 6 men can finish the embroidery work in 3 days.
**Let's assume:**
- Let the work done by 1 woman in 1 day = x.
- Let the work done by 1 man in 1 day = y.
**Calculating the work done:**
- From the given information, we can determine the following equations:
- (2x + 5y) * 4 = 1 (work done by 2 women and 5 men in 4 days).
- (3x + 6y) * 3 = 1 (work done by 3 women and 6 men in 3 days).
**Solving the equations:**
- Simplifying the equations:
- 8x + 20y = 1
- 9x + 18y = 1
- Multiplying the second equation by 2 to make the coefficients of x equal:
- 18x + 36y = 2
- Subtracting the first equation from the second equation:
- (18x + 36y) - (8x + 20y) = 2 - 1
- 10x + 16y = 1
- Simplifying the equation:
- 5x + 8y = 0.5
- Multiplying the equation by 2 to eliminate the decimals:
- 10x + 16y = 1
- Solving the equations:
- 10x + 16y = 1
- 9x + 18y = 1
- Subtracting the second equation from the first equation:
- (10x + 16y) - (9x + 18y) = 1 - 1
- x - 2y = 0
- Solving for x:
- x = 2y
- Substituting the value of x in the equation 5x + 8y = 0.5:
- 5(2y) + 8y = 0.5
- 10y + 8y = 0.5
- 18y = 0.5
- y = 0.5/18
- y = 1/36
**Calculating the time taken by 1 woman alone:**
- Substituting the value of y in the equation x = 2y:
- x = 2(1/36)
- x = 1/18
- Therefore, 1 woman alone can finish the embroidery work in 1/18 days.
**Calculating the time taken by 1 man alone:**
- Since y = 1/36, 1 man alone can finish the embroidery work in 1/(1/36) = 36 days.
Community Answer
2 women and 5 men can together finish an embroidery work in 4 days, wh...
Let the work done by man and woman per day be x and y respectively.
When the work is completed in 4 days
Since 5 men and 2 women complete the work in 4 days
therefore work done by 5 men and 2 women in 1 day =
1/4
∴5x+2y= 1/4 ( equation -i)
When the work is completed in 3 days
Since 6 men and 3 women complete the work in 3 days
therefore work done by 6 men and 3 women in 1 day =
1/3
∴6x+3y= 1/3( equation ii)
Multiplying by 3 in eq i
we get
⇒15x+6y= 3/4 (equation iii)
Multiplying by 2 in equation ii
, we get
⇒12x+6y= 2/3 (equation iv)
On subtracting eq iv from eq iii
we get
⇒15x+6y−12x−6y= 3/4-2/3
⇒3x= 1/12
⇒x= 1/36
On substituting the value of x in eq ii we get
⇒6×1/36 + 3y = 1/3
3y = 1/3-1/6
⇒y= 1/18
Thus,
work done by 1 man in 1 day = 1/36
days
∴ Time taken by 1 man alone to finish the work =36 days
work done by 1 woman in 1 day = 1/18
days
∴ Time taken by 1 woman alone to finish the work =18 days
When the work is completed in 4 days
Since 5 men and 2 women complete the work in 4 days
therefore work done by 5 men and 2 women in 1 day =
1/4
∴5x+2y= 1/4 ( equation -i)
When the work is completed in 3 days
Since 6 men and 3 women complete the work in 3 days
therefore work done by 6 men and 3 women in 1 day =
1/3
∴6x+3y= 1/3( equation ii)
Multiplying by 3 in eq i
we get
⇒15x+6y= 3/4 (equation iii)
Multiplying by 2 in equation ii
, we get
⇒12x+6y= 2/3 (equation iv)
On subtracting eq iv from eq iii
we get
⇒15x+6y−12x−6y= 3/4-2/3
⇒3x= 1/12
⇒x= 1/36
On substituting the value of x in eq ii we get
⇒6×1/36 + 3y = 1/3
3y = 1/3-1/6
⇒y= 1/18
Thus,
work done by 1 man in 1 day = 1/36
days
∴ Time taken by 1 man alone to finish the work =36 days
work done by 1 woman in 1 day = 1/18
days
∴ Time taken by 1 woman alone to finish the work =18 days
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2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.?
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2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.?.
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.?.
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