Question

19) If P and Q together can complete a job in 3 days while
P alone can do the same in 12 days, then how many days
would be required by Q to do the job alone?
A) 3 days
B) 4 days
C) 6 days
D) 12 days​

Answer 1

Given:-

• If P and Q together can complete a job in 3 days while P alone can do the same in 12 days.

To find:-

• Days would be required by Q to do the job alone.

Solution:-

Let,

• P and Q can complete the job in x days and y days respectively.

According to the question,

→ 3/x + 3/y = 1

→ 1/x + 1/y = 1/3 --------(1)

Then,

→ 12/x = 1

→ 1/x = 1/12 --------(2)

Now,

→ 1/y = 1/3 - 1/12

→ 1/y = 4 - 1/12

→ 1/y = 3/12

→ 1/y = 1/4

→ y = 4

Hence,

• the number of days required by Q to do the job alone is 4 days.

Therefore,

• Option (B) is correct.

Answer 2

Given : P and Q together can complete a job in 3 days while

P alone can do the same in 12 days,

To find : how many days would be required by Q to do the job alone  

A) 3 days

B) 4 days

C) 6 days

D) 12 days​

Solution:

P alone can do the same in 12 days,

=> P 1 day work  = 1/12

P alone can do the same in Q days,

=> Q 1 day work  = 1/Q

P and Q together can complete a job in 3 days

=>  P and Q 1 day work  = 1/3

1/12 + 1/Q  = 1/3

=> 1/Q  = 1/3 - 1/12

=> 1/Q = ( 4 - 1) / 12

=> 1/Q  = 3/12

=> 1/Q = 1/4

=> Q = 4

Q alone can do the job in 4 Days

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