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ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations

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Question 36 Problems on Simultaneous Linear Equations Exercise 6
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2 men and 5 women can do a piece of work in 4 days, while one man and one woman can finish

it in 12 days. How long would it take for 1 man to do the work?

Answer:

Let’s assume that 1 man takes x days to do work and y days for women.

So, the amount of work done by 1 man in 1 day = 1/x

And the amount of work done by 1 woman in 1 day = 1/y

Now,

The amount of work done by 2 men in 1 day will be = 2/x

And the amount of work done by 5 women in 1 day = 5/y

Then according to the given conditions in the problem, we have

2/x + 5/y = ¼ … (i)

1/x + 1/y = 1/12 … (ii)

Multiplying equation (ii) by 5, we get

5/x + 5/y = 5/12

2/x + 5/y = ¼

(-)—(-)---(-)

3/x = 5/12 – ¼

3/x = (5 - 3)/12

3/x = 2/12 = 1/6

x = 18

Therefore, 1 man can do the work in 18 days.

Video transcript
"hi guys welcome to lido q a video i am vinit your leader tutor bringing you this question on your screen two men and five women can do a piece of work in four days while one man and one woman can finish it in 12 days how long would it take for one man to do the work now we have defined the variables here the number of days taken by one man be x and let the number of days taken by one woman by then the amount of work done by one man in one day will be one by x so work done by two men in one day will be two by x similarly work done by one woman in one day is one by five one by y work done by five women in one day is five by y okay so this should be y now let us look at the solution from the first condition what do we have two men and five men can do a piece of work in four days so if they can do the work in four days amount of work done in one day is one by four so we can say 2 by x plus 5 by y is equal to 1 by 4 yeah and from second condition similarly we can say that 1 by x plus 1 by y is equal to 1 by 12 this is 2 so multiply equation 2 by 5 and subtract 1 from it what do we get so let's do that multiplying 2 into 5 and subtracting 1 from it we get 5 by x plus 5 by y minus 2 by x minus 2 by y is equal to 5 by 12 minus 1 by 4. so this this is 5 sorry this cancels out right so 3 by x is equal to 2 by 12. isn't that right guys taking the else here okay so this implies 2x equals to 36 this implies x is equal to 80 and here we have our answer therefore number of days taken by one man to do the work is equal to 18 days isn't that easy guys if you still have a dog please leave a comment below do like the video and subscribe to our channel i'll see you in our next video until then bye guys keep practicing"
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Exercises
Problems on Simultaneous Linear Equations Exercise 6
Chapters
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Compound Interest
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Factorization
Simultaneous Linear Equations
Problems on Simultaneous Linear Equations
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Triangles
Mid Point Theorem
Pythagoras Theorem
Rectilinear Figures
Theorems on Area
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