Given that :- The average age of three friends A, B, C = 20 years.
Total age of three friends A, B, C = 3 x 20 = 60 years.
The average age of A and B = 19 years.
Total age of of A and B = 2 x 19 = 38 years.
? Age of C = Total age of three friends A , B and C - Total age of of A and B
Age of C = 60 ? 38 = 22 years
Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
Using formula ,
? Weight of new person = Weight of replaced person + n × increase in Average
Weight of new person = 60 + 8 × 1 = 68 kg
Suppose the age of mother be P years and that of daughter's age be Q years.
According to question P + Q = 56 .........(i)
After 4 years, P + 4 = 3 (Q + 4) ? P + 4 = 3Q + 12 ? P ? 3Q = 8 ......(ii)
On solving equations (i) and (ii) , we get
Q = 12 years
? P = 56 ? 12 = 44 years
Hence , the age of mother is 44 years and her daughter's age is 12 years .
The age of sister of Ravi at the time of birth of Ravi's brother = 4 years
Ravi's sister is 4 + 3 = 7 years elder than Ravi.
The age of father at the time of birth of Ravi = 28 + 7 = 35 Years
Suppose the age of son at present = P years
? Present age of the father = Present age of son + 30 years
Present age of the father = P + 30 years
Age of father at the birth of his son = Present age of the father - Present age of son = ( P + 30 ) ? P = 30 years
Suppose the present age of son = P years
The present age of father = Q years
P + Q = 70 ...(i)
According to question, 2(P + 10) = Q + 10
? 2P + 20 = Q + 10
? 2P ? Q = ?10 ....(ii)
From equations (i) and (ii) , we get
3P = 70 ? 10 = 60 ? P = 20 years
? Q = 70 ? 20 = 50 years
Suppose that son's age before 4 years = P
Present age of the son = P + 4
At son's birth father's age = 3(P + 4) = 3P + 12
The father's present age = (3P +12) + (P + 4) = 48
? 4P = 48 years ? 16 = 32
? P = 8 years
Therefore, 4 years ago the boy was = 12 ? 4 = 8 years
The average age of husband, wife and their child 3 years ago = 27 years
Total age of husband, wife and their child 3 years ago = 27 × 3 = 81 years
The average age of wife and the child 5 years ago = 20 years
Total age of wife and child five years ago was 20× 2 = 40 years
? Total age of wife and child 3 years ago
= 40 + (2 × 2)
= 40 + 4 = 44 years
? Age of husband three years ago = Total age of husband, wife and their child 3 years ago - Total age of wife and child 3 years ago
Age of husband three years ago = 81 ? 44 = 37 years
Therefore, the present age of husband = 37 + 3 = 40 years
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