Question

A alone can complete a work in 12 days and B can alone complete the same work in 24 days .in how many days can a and b together complete the same work?
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Answer 1

Question:

A alone can complete a work in 12 days and B can alone complete the same work in 24 days. In how many days can A and B together complete the same work?

Answer:

8 days

Solution:

It is given that;

A alone can complete the work in 12 days.

ie;

=> Time taken by A (alone) to complete the work. = 12 days.

=> One day work of A (alone)

= 1/12 work

Also,

It if given that;

B alone can complete the work in 24 days.

ie;

=> Time taken by B (alone) to complete the work. = 24 days.

=> One day work of B (alone)

= 1/24 work

Now,

=> One day work of A and B together

= One day work of A (alone)

+ One day work of B (alone)

=> One day work of A and B together

= (1/12 + 1/24) work

=> One day work of A and B together

= (2 + 1)/24 work

=> One day work of A and B together

= 3/24 work

=> One day work of A and B together

= 1/8 work

=> Time taken by A and B together to

complete the work = 8 days

Hence,

Time taken by A and B together to complete the work is 8 days .

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Time required for the work to be completed when person A and person B work together = 8 days.

$\bold{\underline{\underline{\huge{\sf{StEp\:by\:stEp\:explaination:}}}}}$

GIVEN :

• Person A alone can complete a work in 12 days.
• Person B can alone can complete the same work in 24 days.

TO FIND :

• Number of days required by person A and person B's to complete the work if they perform the work together.

SOLUTION :

Person A :

Number of days taken to complete the work = 12 days.

•°• Person A's one day work = $\bold{\dfrac{1}{12}}$

Person B :

Number of days taken to complete the work = 24 days.

•°• Person B's one day work = $\bold{\dfrac{1}{24}}$

Person A + Person B :

Now, if they would work together to perform the work and complete it then the number of days will be the sum of person A's one day work and person B's one day work.

Let's constitute it mathematically,

$\rightarrow$ $\bold{\sf{A's\: one\: day\:work\:+\:B's\:one\: day\: work}}$

Block in the values,

$\rightarrow$ $\bold{\dfrac{1}{12}}$ + $\bold{\dfrac{1}{24}}$

$\rightarrow$$\bold{\dfrac{24+12}{12\times\:24}}$

$\rightarrow$ $\bold{\dfrac{24+12}{288}}$

$\rightarrow$ $\bold{\dfrac{36}{288}}$

$\rightarrow$ $\bold{\dfrac{1}{8}}$

•°• Time required by person A and person B to complete the work together is 8 days.