Question

A,B & C can do a work in 15 hr, 12hr & 20hr respectively. At 4.00 pm ,they start working together and after working for 2 hr , A left the work and B left 2 hr before the completion of the work. In what time the whole work will be completed ?​

Answer 1

Answer:

Step-by-step explanation:

In such questions we may take LCM of each i.e. 12 and 18 which is 36

We assume as 36 units of work (say some 36 toys to be made) is The Complete Work

Since A takes 12 hour, he makes 3 units each hour

Since B takes 18 hours to prepare 36 units, he makes 2 units each hour

Starting with A followed by B, in first 2 hours 5 units made, in next 2 hours, 5 more and so on till 35 units in 7x2 =14 hours…

A will take 1/3hour to make 36th unit i e. 20 min.

So time taken to complete 36 units of work is 14(1/3) hours

Or 14 hour 20 minutes

So starting from 8 am it will be 8 pm after 12 hours and 10:20 pm after 14hr 20 min.

Answer 2

The time taken to complete the work = 8 2/7 hrs

Given:

A can do a work in 15 hrs

B can do a work in 12 hrs

C can do a work in 20 hrs

They started worked together for 2 hr  

A left the work after 2 hrs and B left the work 2 hr before the completion of the work.  

To find:

In what time the whole work will be completed

Solution:  

Given A can do a work in 15 hrs  

⇒ The work can done by A in 1hr = 1/15

B can do a work in 12 hrs  

⇒ The work can done by B in 1hr = 1/12  

C can do a work in 20 hrs  

⇒ The work can done by C in 1hr = 1/20

The work can be done by A, B and C in 1hr

=  $\frac{1}{15}+ \frac{1}{12} +\frac{1}{20}$ = $\frac{4+5+3}{60}$ =  $\frac{4+5+3}{60} = \frac{12}{60} = \frac{1}{5}$  

Given that A, B and C worked together for 2 hr  

The work can be done in 2hrs = $2( \frac{1}{5} ) = \frac{2}{5}$    

A, B and C worked together for 2 hr and completed $\frac{2}{5}$      

Let assume that B and C worked for x hrs

The work can be done by A and C together in x hrs  

= $x(\frac{1}{15} + \frac{1}{20}) = x(\frac{4+3}{60} )= x(\frac{7}{60})$  

The work can be done by A and C together in x hrs = $x(\frac{7}{60})$

B left 2hrs before the completion of the work which means last 2 hrs work is done by C

⇒ The work can be done C in last 2 hrs = $2( \frac{1}{20}) = \frac{1}{10}$  

As we know total work = 1

⇒  $\frac{2}{5} + x(\frac{7}{60}) + \frac{1}{10}$ = 1

⇒  $\frac{24+7x + 6}{60}= 1$  

⇒ $7x +30= 60$

⇒ 7x = 30

⇒ x = 30 /7 hrs

Therefore, The time taken to complete the work

= 2 hrs + 2 hrs + 30 /7 hrs

= 4 hrs + 30/7 hrs

= $\frac{28 + 30}{7}$ hrs = $\frac{58}{7}$  =  $8 \frac{2}{7}$ hrs  

The time taken to complete the work = 8 2/7 hrs

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