Question

Vicky can finish the work in 10 days, bala can finish the work in 12 days, and venkat can finish the work in 15 days. They all start to work together. Vicky leaves the work after two days and bala leaves 3 days before the work was completed. How long did it take for the work to be completed?

Answer 1

Answer:

13

Step-by-step explanation:

Answer 2

The answer is 6 days

Given: Vicky can finish the work in 10 days

Bala can finish the work in 12 days

Venkat can finish the work in 15 days

They all started the work together

Vicky leaves the work after 2 days

Bala leaves the work before completing 3 days

To find: How many days it will take to complete the work

Solution:

From given data

Vicky can finish the work in 10 days

⇒ the work can be done by Vicky in 1 day = 1/10

Bala can finish the work in 12 days

⇒ the work can be done by Bala in 1 day = 1/12

Venkat can finish the work in 15 days

⇒ the work can be done by Venkat in 1 day = 1/15

⇒ the work can be done by them together in 1 day = $\frac{1}{10} +\frac{1}{12}+ \frac{1}{51}$

= $(\frac{3+5+4}{60} ) = \frac{12}{60}$  

They all started the work together and Vicky leaves the work after 2 days

which means they worked together for two days

⇒ the work can be done in 2 days = $2 ( \frac{12}{60})$ = $\frac{12}{30}$  

After that Venkat and Bala worked together

Assume Bala and Venkat worked for x days

⇒ then the work done by Bala and venkat in x days = $x(\frac{12}{30})$  

Bala leaves the work before completing 3 days which means last 3 days work is done by Venkata  

⇒ the work done by Venkata in 3 days = $3(\frac{1}{15})$ = $\frac{1}{5}$  

Here, the total work = 2 days work + x days work + 3 days

⇒ = $\frac{12}{30}$ + $x(\frac{12}{30})$+ $\frac{1}{5}$  = 1

⇒  $\frac{12+12x+6}{30}$ = 1

⇒ 12+ 12x + 6 = 30

⇒ 12x = 30 -18

⇒ 12x = 12

⇒ x = 1

⇒ Bala and Venkat worked for 1 days  

The number of days to complete the work = 2 + 1 + 3 = 6 days

Therefore, the number of days to complete the work = 6 days

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