Question

plz solve this question urgently please plz plz answer correctly I will mark you the brainliest
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plz answer both the questions correctly
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Answer 1

Question#1

2 men and 5 boys can do a piece of work in 4 days while 4 men and 4 boys can do it in 3 days. How long would it take one man alone to do it and How many days would it take for one boy alone to do it?

Solution

Let,

time taken by

one man to complete the work = x days   and

one boy to complete the work = y days

then,

work done by 1 man = 1 / x

and work done by one boy  = 1 / y

so,

work done by 2 men = 2(1/x) = 2/x

work done by 5 boys = 3(1/y) = 3/y

also, work done in 4 days = 1 / 4

hence,

${\tt{\frac{2}{x}+\frac{5}{y}=\frac{1}{4}}$

$\tt 2(\frac{1}{x})=\frac{1}{4}-\frac{5}{y}\\\\\tt 2(\frac{1}{x})=\frac{y-20}{4y} \\\\\boxed{\tt \frac{1}{x}=\frac{y-20}{8y}}....eqn(1)$

Now,

work done by 4 men = 4(1/x)=4/x

work done by 4 boys = 4(1/y)=4/y

also,work done in 3 days = 1/3

hence,

$\tt \frac{4}{x}+\frac{4}{y}=\frac{1}{3}\\\\\tt 4(\frac{1}{x}+\frac{1}{y})=\frac{1}{3}\\\\\frac{1}{x} + \frac{1}{y}= \frac{1}{12}\\\\\tt now\:substituting\:eqn(1) \;here\\\\\tt \frac{y-20}{8y} \: +\frac{1}{y}=\frac{1}{12}\\\\\tt \frac{y-20+8 }{8y}=\frac{1}{12}\\\\\tt cross\:multiplying\\\\\tt 12(y-12) = 8y\\\\\tt 12 y - 144 = 8y\\\\ \boxed{\tt y=36 }$

putting value of y in eqn(1)

$\tt \frac{1}{x}=\frac{36-20}{8(36)}\\\\\tt \frac{1}{x}=\frac{16}{288}\\\\\boxed{\tt x = 18}$

Therefore, time taken by 1 man to complete the work is 18 days

and time taken by 1 boy to complete the work is 36 days.

_______________________________________

Question#2

Solve graphically x - y = 1 ; 2 x + y = 8 . shade the area bound by these two lines and the y-axis . Also determine its area.

Solution

→In eqn x- y = 1

taking x = 1 ; y = 0

taking x = 2 ; y = 1

taking x = 3 , y = 2

→In eqn 2 x + y = 8

taking x = 1 , y = 6

taking x = 2 , y = 4

taking x = 3 , y  = 2

The graph is in the attachment

Area of shaded region = 1/2 * height*base

ar(shaded region) = 1/2*2*3

ar(shaded region) = 3 sq. units.