Question

1) 2 Gents and 5 Ladies complete a work in 4 dyas. 4 Gents and 4 Ladies takes 3
days to complete the same work. Then how many days need to complete the
same work for a single Gents or Ladies?​

Answer 1

Step-by-step explanation:

Let one women takes xx days to finish the work and one man takes yy days to finish the work .

According to the question.

\begin{array}{l} \dfrac { 2 }{ x } +\dfrac { 5 }{ y } =\dfrac { 1 }{ 4 } \\ 4\left( { 2y+5x } \right) =xy \\ 8y+20x=xy......\left( 1 \right) \end{array}

x

2

+

y

5

=

4

1

4(2y+5x)=xy

8y+20x=xy......(1)

Now,

\begin{array}{l} \dfrac { 3 }{ x } +\dfrac { 6 }{ y } =\dfrac { 1 }{ 3 } \\ \Rightarrow 9y+18x=xy.........\left( 2 \right) \\ \left( 1 \right) \times 9-\left( 2 \right) \times 8 \\ \left( { 8y+20x=xy } \right) 9...............\left( 3 \right) \\ \left( { 9y+18x=xy } \right) 8...............\left( 4 \right) \\ \, \, \, \, \, \, \, \, \, eq\left( 3 \right) -\left( 4 \right) \\ 72y+18x=9xy \\ 72x+144x=8xy \\ \underline { -\, \, \, \, \, \, \, \, -\, \, \, \, \, \, \, \, \, \, \, \, \, -\, \, \, \, \, \, } \\ \, \, \, \, \, \, \, \, \, \, \, \, \, \, 36x=xy \\ y=36 \end{array}

x

3

+

y

6

=

3

1

⇒9y+18x=xy.........(2)

(1)×9−(2)×8

(8y+20x=xy)9...............(3)

(9y+18x=xy)8...............(4)

eq(3)−(4)

72y+18x=9xy

72x+144x=8xy

−−−

36x=xy

y=36

Putting y=36y=36 in equation (1)(1)

We get x=18x=18

One man and one women will do work in dd days.

\dfrac{1}{{36}} + \dfrac{1}{{18}} = \dfrac{1}{d}

36

1

+

18

1

=

d

1

Hence,

d=12d=12 days.