Question 73

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 ?

Solution

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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