Question

Ram can do a piece of work in I2 days and Shyam can do the same work in16 days. They both started work together,
Ram left 2 days before the completion of work. Then total work is completed on
in how many days ?
​

Answer 1

AnswEr :

Let the Total Work completed in x days.

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\tt Ram's\:Work + Shyam's\:Work = Total\:Work\\\\\\:\implies\tt \dfrac{Time}{Ram's\:Rate}+\dfrac{Time}{Shyam's\:Rate}=1\\\\\\:\implies\tt \dfrac{(x-2)}{12}+\dfrac{x}{16}=1\\\\\\:\implies\tt\dfrac{4(x - 2) + 3x}{48} = 1\\\\\\:\implies\tt \dfrac{4x - 8 + 3x}{48} = 1\\\\\\:\implies\tt7x - 8 = 48\\\\\\:\implies\tt7x = 48 + 8\\\\\\:\implies\tt 7x = 56\\\\\\:\implies\tt x = \dfrac{56}{7}\\\\\\:\implies \underline{\boxed{\tt x = 8 \:Days}}$

⠀

$\therefore\:\underline{\textsf{Hence, Total Work completed in \textbf{8 Days.}}}$

Answer 2

||✪✪ QUESTION ✪✪||

Ram can do a piece of work in I2 days and Shyam can do the same work in16 days. They both started work together,

Ram left 2 days before the completion of work. Then total work is completed on in how many days ?

|| ✰✰ ANSWER ✰✰ ||

Lets Solve it without x . .

Given That, Ram can do a piece of work in I2 days and Shyam can do the same work in16 days.

So, we will take LCM of both days as our Total work that needs To be Done.

→ LCM of 12 and 16 = 48 units= Let Total work.

Now, As A complete the Whole work in 12 days.

So,

→ Efficiency of A = (48/12) = 4 unit/day.

And,

→ Efficiency of B = (48/16) = 3 unit/day.

So, we can say That,

→ A + B per day work = (4+3) = 7 units.

_____________________

Now, Given That, Ram left 2 days before the completion of work.

So, we can say That, In last 2 days only B alone did Some work .

So,

→ in Last 2 days B did = 3*2 = 6 units of work.

______________________

Now, we can say That, Left work done by (A+B) Both now,

So,

→ Left work = 48 - 6 = 42 units .

And,

→ This Left work now, done by (A+B) in = 42/7 = 6 days.

______________________

So,

→ Total Number of Days To complete whole work = 6 days by (A+B) + 2 days by B alone = 8 days.

Hence, total work is completed 8 days ..