Question

Garima and her sister together can paint the walls of their house in 45 days. If Garima alone did job it would have taken her 81 Day.if dou start painting together but garimas sister had to leave 9 days before completing the work

Answer 1

Answer: 49 days

Step-by-step explanation:

Garima and her sister can paint the wall = 45 days

Garima alone can paint the wall = 81 days

Therefore,

Work done by (Garima + her sister) in 1 day = 1/45

And,  

Work done by Garima alone in 1 day = 1/81

Also, given that, they start painting together but garima’s sister had to leave 9 days before the completion of the work.

So, if we consider that the entire work is done in “x” days.

Then, they both Garima & her sister works for “(x – 9) days” and the remaining 9 days of work is done by Garima alone.  

According to the assumption, we can write the equation as,

(x - 9)/45 + 9/81 = 1

⇒ (x - 9)/45 + 1/9 = 1

⇒ 9x – 81 + 45 = 45 * 81

⇒ 9x – 36 = 405

⇒ 9x = 405 + 36

⇒ x = 441 / 9 = 49 days

Thus, it would take 49 days by the sisters to paint the walls of their house.

Answer 2

Answer:

65 days.

Step-by-step explanation:

Garima alone can complete the job in 81 days.

Portion of work done by Garima in 1 day= 1/81

Portion of work done by Garima in 45 day= 45/81

Garima and her sister together can complete the job in 45 days.

Portion of work done by Garima's sister in 45 day= 1-45/81=$1-\frac{45}{81}=\frac{(81-45)}{81}=\frac{36}{81}$

Portion of work done by Garima's sister in 1 day= (36/81)÷45=4/405

Portion of work done by Garima's sister in 9 day= 9×(4/405)=4/45

Now Garima can complete 4/5th portion of work in (4/5)÷(1/81)=(4×81)÷5=324/5=64.8 days≈65days.

Therefore Garima has to work for 65 days more after her sister left to complete the job.