Question

A and B can finish a Piece of work in 6and 10 days respectively . A began the work and worked at it for 2 days . he was Then joined by B. Find the tot el time taken to Complete the work

Answer 1

Answer :

›»› The total time taken to complete the work is 4.5 days.

Given :

• A and B can finish a Piece of work in 6and 10 days respectively . A began the work and worked at it for 2 days . he was Then joined by B.

To Find :

• The total time taken to complete the work.

Solution :

Let us assume that, the work is x.

→ Work done A in one day = x/6

→ Work done by B in one day = x/10

→ Work done by A in two days = 2x/6

→ Work done by A and B in one day = x/6 + x/ 10

→ Work done by A and B in one day = 8x/30

→ Work left = x - 2x/6

Time taken by both A nad B,

→ 4x/6 ÷ 8x/30

→ 2x/3 ÷ 8x/30

→ 2x/3 ÷ 4x/15

→ 2x/3 * 15/4x

→ 2x * 5/4x

→ 5/2

→ 2.5

Now,

→ Total time = 2.5 + 2

→ Total time = 4.5

Hence, the total time taken to complete the work is 4.5 days.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• A can finish work in 6 days

$\:\:$

• B can finish work in 10 days

$\:\:$

• A started work 2 days before B

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• Total time taken to complete the work

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the total days required be "x"

$\:\:$

$\underline{\bold{\texttt{One day work of A :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf \dfrac { 1 } { 6 }$

$\:\:$

$\underline{\bold{\texttt{One day work of B :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf \dfrac { 1 } { 10 }$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

• A works from the very beginning , So A will work for (x) days

$\:\:$

• B works 2 days less than A , So B works for (x - 2) days

$\:\:$

$\sf \longmapsto 1 = \dfrac { 1 } { 6 } \times (x) + \dfrac { 1 } { 10 } \times (x - 2)$

$\:\:$

$\sf \longmapsto 1 = \dfrac { 5x + 3x - 6} { 30 }$

$\:\:$

$\sf \longmapsto 1 = \dfrac { 8x - 6 } { 30 }$

$\:\:$

$\sf \longmapsto 30 = 8x - 6$

$\:\:$

$\sf \longmapsto 30 + 6 = 8x$

$\:\:$

$\sf \longmapsto x = \dfrac { 36 } { 8 }$

$\:\:$

$\bf \dashrightarrow 4.5$

$\:\:$

• Hence total days required to complete the work is 4.5