5 Men are living in a home. The average age of the five men before 5 years was 55. After P years, one new man aged 50 joins with others in the house which makes the average age 60. Find the value of P.
Let the total age of 5 men be X.
Then the average age of 5 men before 5 years = (X - number of years x number of men) / number of men = (X - 3x5)/5 = (X-15)/5 = 55
Then X = 55 x 5 + 15 = 290.
i.e., Presently the total age = 290.
After P years, the total age of the 5 men becomes X + 5xP = 290 + 5xP.
One man aged 50 joins with them. Therefore the average becomes (Total age of original 5 men after P years + Age of new man) / Total number of men = (290+5P+50)/(5+1) = 60
Or 5P = 360-340 = 20
p = 20/5 = 4
Therefore, 4 years is our required answer.
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