Question

. A can do a work in 36 days and B in 32
days. If they work on it together for 12
days, then what fraction of work is
left?​

Answer 1

GIVEN :-

• Number of days taken by A to complete the work = 36 days
• Number of days taken by B to complete the work = 32 days
• Number of days A and B worked together = 12 days

TO FIND :-

• The fraction of work left

SOLUTION :-

Work done by A in one day = $\sf\dfrac{1}{36}$

Work done by B in one day = $\sf\dfrac{1}{32}$

Work done by both A and B in one day

= $\sf\dfrac{1}{36}$ + $\sf\dfrac{1}{32}$

= $\sf\dfrac{17}{288}$

Work done by both A and B in 12 days

= $\sf{12\times \dfrac{17}{288}}$

= $\sf{\dfrac{17}{24}}$

The fraction of work left = $\sf{1-\dfrac{17}{24}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf{\dfrac{7}{24}}$

Hence , The fraction of work left is $\sf{\dfrac{7}{24}}$

Answer 2

Answer:

Given :-

• A can do a work in 36 days and B in 32 days.
• If they work on it together for 12 days.

To Find :-

• What is the fraction of work left.

Solution :-

A's work done in one day = $\dfrac{1}{36}$

And, B's work done in 12 days = $\dfrac{1}{32}$

According to the question,

➠ A and B work done in 1 days together,

⇒ $\dfrac{1}{36}$ + $\dfrac{1}{32}$

⇒ $\dfrac{8 + 9}{288}$

⇒ $\dfrac{17}{288}$

➠ A and B work done in 12 days together,

⇒ $\dfrac{17}{288}$ × 12

⇒ $\dfrac{17}{24}$

Hence, the fraction of work left,

⇒ 1 - $\dfrac{17}{24}$

⇒ $\dfrac{7}{24}$

∴ The fraction of work left is $\boxed{\bold{\large{\dfrac{7}{24}}}}$

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