Question

The average age of a group of six girls is 12 years 10 months. One leaves the group and the average is decreased by 2 months. How old is the girl who leaves the group?

Answer 1

Answer: The girl is 13 years and 8 months old

The average of age of the six girls is:

$\frac{A+B+C+D+E+F}{6}=154$ 

Why 154? Is the conversion of 12 years + 10 months

$12y*\frac{12m}{1y} =144months+10months=154months$

So: A+ B + C + D + E + F = 154  × 6

A+ B + C + D + E + F = 924   (I)

Now we propose the new average for 5 girls, with the average decrease by 2 months (152 months):

$\frac{A+B+C+D+E}{5} =152$

A + B + C + D + E = 152 × 5

(A + B + C + D + E) = 760    (II)

We replace II in I:

760 + F = 924

F = 924 - 760

F = 164

We do the conversion in years:

$164m* \frac{1y}{12m} =13.66years$

Conversion in months:

$0.66y* \frac{12m}{1y}=7.9months=8months$

We can conclude that girl is 13 years and 8 months old