Question

Raj can do a piece of work in 15 days and Ram in 20 days . With the help of John , the work gets finished in 5 days . How long will John take to finish the work alone​

Answer 1

Answer:

The number days John takes to finish the work alone is 12 .

Step-by-step explanation:

Given as :

Raj can do a piece of work in 15 days

So, Raj 1 day work = $\dfrac{1}{15}$

Ram can do a piece of work in 20 days.

So, Ram 1 day work = $\dfrac{1}{20}$

With the help of John , the work is completed in 5 days

Let  john 1 day work = $\dfrac{1}{d}$

According to question

Raj 1 day work +  Ram 1 day work  + john 1 day work = total days to finish work

i.e $\dfrac{1}{15}$  +  $\dfrac{1}{20}$ + $\dfrac{1}{d}$  = $\dfrac{1}{5}$

Or, $\dfrac{1}{d}$ = $\dfrac{1}{5}$ - ( $\dfrac{1}{15}$  +  $\dfrac{1}{20}$ )

Or, $\dfrac{1}{d}$ = $\dfrac{1}{5}$ - ( $\dfrac{4+3}{60}$ )

Or, $\dfrac{1}{d}$ = $\dfrac{1}{5}$ - $\dfrac{7}{60}$

Or, $\dfrac{1}{d}$ = $\dfrac{12-7}{60}$

Or, $\dfrac{1}{d}$ = $\dfrac{5}{60}$

Or, $\dfrac{1}{d}$ = $\dfrac{1}{12}$

∴ d = 12

So, The number days John takes to finish the work alone = d = 12

Hence, The number days John takes to finish the work alone is 12 . Answer