Question

A mother can do a certain job in x hours. Her daughter takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the mother take to do the job ?
A) 3
B) 6
C) 9
D) 12

Answer 1

✏✏✏.A mother can do a certain job in x hours. Her daughter takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the mother take to do the job ?
A) 3
B) 6
C) 9✔✔✔
D) 12

Answer 2

A mother can do a certain job in x hours. Her daughter takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the mother take to do the job ?
A) 3
B) 6
C) 9
D) 12


Answer:   C) 9 


$\underline{\underline{\Huge\mathfrak{Solution-}}}$


➡️The mother completes the job in x hours.
So, the daughter will take 2x hours to complete the same job.

 

➡️In an hour, the $\bold{mother}$
will complete 1/x of the total job.

➡️In an hour, the$\bold{daughter}$ will complete 1/2x of the total job.

 

☣️So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.

i.e., in an hour they will complete 3/2x of the job.

 

➡️The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6 th of the task in an hour.

 

Equating the two information, we get
$\frac{3}{2x} = \frac{1}{16}$



➡️By solving for x, we get 2x = 18 or x = 9.

 

➡️The mother takes 9 hours to complete the job.