P and q can do a work in 12 days and 16 days respectively p started the work alone after how many days should q join p so that the work is finished in 9 days
Answers
Answer:
Q should join P after 5 days so that work is completed in 9 days.
Step-by-step explanation:
P can do the work in 12 days
=> Fraction of work done by P in 1 day = 1/12
Q can do the work alone in 16 days
=> Fraction of work done by Q in 1 day = 1/16
When P and Q work together,
Fraction of work done by P+Q in 1 day = 1/12 + 1/16 = 7/48
Let us assume that P works alone for "x" days.
As the work needs to be completed in 9 days, Q will join after (9 - x) days.
This means:
P will work alone for x days
P+Q will work together for (9 - x) days
Fraction of work done by P in "x" days = x/12
Fraction of work done by (P+Q) in (9-x) days = (7/48)*(9 - x)
Both these fractions when added represented completion of work
=>
=> 4x + 7*(9 - x) = 48
=> 4x + 63 - 7x = 48
=> -3x = -15
=> x = 5
P should work alone for 5 days and Q should join on the 6th day.
Final answer: Q should join P after 5 days so that work is completed in 9 days.