The average age of a group of 20 men is 30 years. A 50 year old man leaves the group, while a woman joins the group. The average age decreases by 1 year. What is the age of the woman ?
Given that the average age of 20 men is 30 years
$$\frac{sum\ of\ ages}{20}$$=30
sum of ages =600
a man of 50 years leaves
so 600-50=550
a woman adds to the group and the average decreases by a year
let the age of woman be k
so $$\frac{\left(550+k\right)}{20}$$=29
=>550+k=580
=>k = 30
therefore age of the woman is 30
Hence answer is option B
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