Question

Saurabh can complete a work in 18 hours while Vinod can complete the same work in 24 hours. How long will it take them together to complete the work if Saurabh is called away 2 hours before the completion of work, while Vinod continues with work​

Answer 1

Answer:

$\boxed{\frac{80}{7}}$

Step-by-step explanation:

→ Let Vinod continues the work = x hours

→ So, now Saurabh can do the work = (x - 2) hours

→ Work done by Saurabh in 1 hour = 1/18

→ Then, work done by Saurabh in (x - 2) hours = x - 2/18

→ Work done by Vinod = x/24

→ Now, work done by both them together = x - 2/18 + x/24

Here, we can see that the whole work 1 is completed. So,

→ x - 2/18 + x/24 = 1

= 4x - 8 + 3x/72 = 1

Now, we will take 72 in the opposite side and multiply it with 1, as it was in division so when we will change it,it will be in the form of multiplication.

= 4x - 8 + 3x = 72

= 7x - 8 = 72

= 7x = 72 + 8

= 7x = 80

= x = 80/7

We can write it in the form of mixed fraction.

= x = 11 whole 3/7

$\mathrm{\therefore They\:together\: finished\:the\:work\:in\:80/7 \:hours \:or \:11 \:whole \:3/7 \:hours.}$

_________________________

Answer 2

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

$\:\:$

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

$\:\:$

• Saurabh can complete a work in 18 hours

$\:\:$

• Vinod can complete the same work in 24 hours

$\:\:$

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

$\:\:$

How long will it take them together to complete the work if Saurabh is called away 2 hours before the completion of work, while Vinod continues with work

$\:\:$

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

$\:\:$

Let Vinod continues the work = x hours

$\:\:$

Saurabh can do the work = (x - 2)hours

[Saurabh is called away 2 hours before]

$\:\:$

$\underline{\bold{\texttt{Work done in 1 hr.}}}$

$\:\:$

Saurabh in 1 hour = $\sf \dfrac { 1} { 18 }$

$\:\:$

Saurabh in (x - 2) hours = $\sf \dfrac { x - 2} { 18 }$

$\:\:$

Work done by Vinod = $\sf \dfrac { x } { 24 }$

$\:\:$

Now, work done by both them together = $\sf \dfrac { x - 2} { 18 } + \dfrac { x } { 24 }$

$\:\:$

Here, we can see that the whole work 1 is completed.

$\:\:$

$\sf \longmapsto \dfrac { x - 2} { 18 } + \dfrac { x } { 24} = 1$

$\:\:$

$\sf \longmapsto \dfrac { 4x - 8 + 3x } { 72 } = 1$

$\:\:$

$\sf \longmapsto 4x - 8 + 3x = 72$

$\:\:$

$\sf \longmapsto 7x - 8 = 72$

$\:\:$

$\sf \longmapsto 7x = 72 + 8$

$\:\:$

$\sf \longmapsto 7x = 80$

$\:\:$

$\sf \longmapsto x = \dfrac { 80 } { 7}$

$\:\:$

$\bf \dashrightarrow x = 11 \dfrac { 3} { 7 }$

$\:\:$

$\sf \therefore They\:together\: finished\:the\:work\:in \\ \\ \sf \dfrac { 80} { 7} \:hours \:or \:11\dfrac { 3} { 7} \:hours.$

$\rule{200}5$