Question

Average age of a, b and c is 84 years, however when d joins them then the average comes down to 80. Now a new person e whose age is 3 years more than d replaces a and the new average is 79 years. What is the age of a

Answer 1

Answer:

75

Step-by-step explanation:

$\frac{a + b + c}{3} = 84 \\ a + b + c = 252 \\ \\ \frac{a + b + c + d}{4} = 80 \\ a + b + c + d = 320 \\ 252 + d = 320 \\ d = 320 - 252 = 68 \\ age \: of \: d \: = 68 \\ \\ a \: is \: replaced \: by \: e \\ e \: is \: 3 \: years \: older \: than \: d \: 68 + 3 = 71 \\ \frac{b + c + d + e}{4} = 79 \\ b + c + d + e = 79 \times 4 \\ b + c + 68 + 71 = 316 \\ b + c = 316 - 139 = 177 \\ \\ a + b + c = 252 \\ a + 177 = 252 \\ a = 252 - 177 = 75$

a age is 75 years