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3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically are​
  • a)
    15u + 30v – 1 = 0; 16u + 28v – 1 = 0
  • b)
    15x – 30y + 1 = 0; 16x + 28y +1 = 0
  • c)
    16u + 30v – 1 = 0; 16u + 28v – 1 = 0
  • d)
    16x + 30y – 1 = 0; 16x + 28y – 1 = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
3 women and 6 men can together finish a tailoring job in 5 days, while...
Let's assume that one woman can do the job in x days, and one man can do the job in y days.

From the first statement, we can write the following equation:

3x + 6y = 1/5

This is because in 5 days, the 3 women and 6 men can do 1 job.

From the second statement, we can write another equation:

4x + 7y = 1/4

This is because in 4 days, the 4 women and 7 men can do 1 job.

Now we have two equations with two unknowns. We can solve for x and y using any method of solving linear equations.

Multiplying the first equation by 4 and the second equation by -5, we can eliminate x and solve for y:

12x + 24y = 4/5

-20x - 35y = -1/4

-8x - 16y = -1/5 (multiplying the first equation by -2)

-20x - 35y = -1/4

Now we can solve for y:

-8x - 16y = -1/5

-20x - 35y = -1/4

Multiplying the first equation by -35/16, we get:

35/40x + 35/40y = 7/40

-20x - 35y = -1/4

Adding the two equations, we get:

15/40x - 0y = 6/40

Simplifying, we get:

3/8x = 3/20

x = 3/8 * 20/3 = 5/2

Therefore, one woman can do the job in 5/2 = 2.5 days.

To find y, we can substitute x = 5/2 into one of the equations:

3x + 6y = 1/5

3(5/2) + 6y = 1/5

15/2 + 6y = 1/5

Multiplying both sides by 10, we get:

750/2 + 60y = 2

60y = -746/5

y = -373/150

Since y cannot be negative, we made an error somewhere. Checking our calculations, we can see that we made a mistake when we multiplied the first equation by -2. It should be:

-6x - 12y = -2/5

-20x - 35y = -1/4

Multiplying the first equation by -5/2, we get:

15/40x + 15/40y = 3/20

-25/2x - 35/2y = -1/4

Adding the two equations, we get:

-25/2x - 5/2y = -1/5

Simplifying, we get:

5x + y = 2/5

Substituting x = 5/2 into this equation, we get:

5(5/2) + y = 2/5

25/2 + y = 2/5

Multiplying both sides by 10, we get:
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3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically area)15u + 30v – 1 = 0; 16u + 28v – 1 = 0b)15x – 30y + 1 = 0; 16x + 28y +1 = 0c)16u + 30v – 1 = 0; 16u + 28v – 1 = 0d)16x + 30y – 1 = 0; 16x + 28y – 1 = 0Correct answer is option 'A'. Can you explain this answer?
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3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically area)15u + 30v – 1 = 0; 16u + 28v – 1 = 0b)15x – 30y + 1 = 0; 16x + 28y +1 = 0c)16u + 30v – 1 = 0; 16u + 28v – 1 = 0d)16x + 30y – 1 = 0; 16x + 28y – 1 = 0Correct answer is option 'A'. Can you explain this answer? 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 3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically area)15u + 30v – 1 = 0; 16u + 28v – 1 = 0b)15x – 30y + 1 = 0; 16x + 28y +1 = 0c)16u + 30v – 1 = 0; 16u + 28v – 1 = 0d)16x + 30y – 1 = 0; 16x + 28y – 1 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically area)15u + 30v – 1 = 0; 16u + 28v – 1 = 0b)15x – 30y + 1 = 0; 16x + 28y +1 = 0c)16u + 30v – 1 = 0; 16u + 28v – 1 = 0d)16x + 30y – 1 = 0; 16x + 28y – 1 = 0Correct answer is option 'A'. Can you explain this answer?.
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