Question

To construct the model of pyramid shaped roof Ram takes 6 days less than Shyam to finish the work. If
both of them together can finish the work in 4 days, then in how many days Shyam can finish the work?
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Answer 1

Answer:

Many many people we use to finish the work

Answer 2

Step-by-step explanation:

Given that: To construct the model of pyramid shaped roof Ram takes 6 days less than Shyam to finish the work. If both of them together can finish the work in 4 days.

To find:In how many days Shyam can finish the work?

Solution:

Let shyam take x days to finish the task.

then ram takes (x-6) days to finish the same task

Shyam alone can do (1/x)th part of work in one day and

Ram alone can do (1/(x-6))th part of work in one day

Both are working together and finish 1/4 th part of work in one day.

Now,form the equation

$\frac{1}{x} + \frac{1}{x - 6} = \frac{1}{4} \\ \\ take \: LCM \\ \\ \frac{x - 6 + x}{x(x - 6)} = \frac{1}{4} \\ \\ \frac{2x - 6}{ {x}^{2} - 6x} = \frac{1}{4} \\ \\ cross \: multiply \\ \\ {x}^{2} - 6x = 8x - 24 \\ \\ {x}^{2} - 6x - 8x + 24 = 0 \\ \\ {x}^{2} - 14x + 24 = 0$

Its a simple quadratic equation, now split the middle term

${x}^{2} - 12x - 2x + 24 = 0 \\ \\ x(x - 12) - 2(x - 12) = 0 \\ \\ (x - 12)(x - 2) = 0 \\ \\ either \:( x - 12) = 0 \\ \\ \bold{x = 12} \\ \\ or \: (x - 2) = 0 \\ \\ \bold{x = 2}$

Thus,Shyam alone can finish the work in 12 days

and ram alone can finish the same project work in (12-6) = 6 days.

Now discard the value x=2(because by putting this value ram alone can finish the work in -4 days,which is not possible)

Hope it helps you.