Question

8 sweepers and 6 house kefers canclean a hall in 14 days. White 12sweepers and to housekeepers canfinish the same work in todays.Suppose one hape keefer alonewants to finish this task find thetaken by him.​

Answer 1

In the above Question, the following information is given -

8 sweepers and 6 housekeepers can clean a hall in 14 days.

12 sweepers and 2 housekeepers can do the same work in 2 days.

Now,

Let us assume that the work is done by a sweeper is x and the work done by a housekeeper is y.

So,

We can write the following equations, from the given information-

8x + 6y = 14.......... { 1 }

12x + 2y = 2........... { 2 }

Multiplying the second equation by 3

=>8x + 6y = 14

=> 36x + 6y = 6

Subtracting

-24x = 8

=> x = -3

( 1 / x ) = ( -1/ 3 )

But, this is not possible.

Hence, we conclude that the given question is wrong...

__________ .

Answer 2

$\huge\sf\pink{Answer}$

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ 8 Sweepers and 6 house keepers can clean a hall in 14 days

✭ 12 sweepers and 2 house keepers can finish the same work in days

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ Time taken to complete the work by a single

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let work done by sweeper be A and work done by house keeper be B

So according to the Question,

➝ 8a + 6b = 14 .... eq(1)

➝ 12a + 2b = 2 .... eq(2)

Multiplying eq(2) with 3,

➢ $\sf 8a + 6b = 14$

➢ $\sf 36a+6b = 6$

Subtracting,

➳ $\sf -24a = 8$

➳ $\sf \red{x = -3}$

But in the next step if you see

➠ $\sf\dfrac{1}{x} = -\dfrac{1}{3}$

But that is absolutely impossible and hence the conclusion is wrong

$\rule{170}3$