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
Given that :- The average age of 19 boys in a class = 21 years
Total age of 19 boys = 19 × 21 = 399 years
The average age of 19 boys and teacher = 22 years
Total age of 19 boys and teacher = 20 × 22 = 440 years
?Teacher's age = Total age of 19 boys and teacher - Total age of 19 boys
Teacher's age = 440 ? 399 = 41 years
Hence , the age of teacher is 41 years .
Suppose the age of son is P years
Therefore, the age of father will be 5P + 1
According to question ,
? 4( age of son + 3 ) ? 2 years = age of father + 3 years
? 4 ( P + 3 ) ? 2 = ( 5P + 1 ) + 3
? 4P + 12 ? 2 = 5P + 4
? 10 ? 4 = 5P ? 4P
? P = 6
Age of father = 5P + 1 = 5 × 6 + 1 = 31 years
Hence , the age of father is 31 years .
Suppose the present age of son is P years.
Therefore, present age of the father = 4P years
According to question
The present age of son + 3 years = 15
? The present age of son ( P ) = 15 ? 3 = 12 years
The present age of father = 4P = 4 × 12 = 48 years
? The present age of man's wife = The present age of father - 3 = 48 ? 3 = 45 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 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 .
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
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
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
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