Problems on Ages
1) Rule :
If one person out and another person come in any group and average age is increase of group then age of another person = age of person out + number of person in group X increase average age .
Example :
Average age increase by four years of 8 persons group when one person come at place of 30 years old person .What was the age of new person .
Sol.
Age of new person = age of person out + number of person in group X increase average age
= 30 + 8 X 4
= 62 years
2) Rule :
If one person out and another person come in any group and average age is decrease of group then age of another person = age of person out + number of person in group X decrease average age .
Example :
Average age decrease by 1/9 years of 45 persons group when one person come at place of 60 years old person .What was the age of new person .
Sol.
Age of new person = age of person out - number of person in group X increase average age
= 60 - 45 X 1/9
= 55 years
3) Rule :
If one person come in any group and average age of group increase then age of new person.
= before average + new number X increase average age
Example :
Average age of 6 women is 32 years after joining Reena average age is increase 1 year. What was Reena's age .
Sol.
Reena's age = before average + new number X increase average age
= 32 + (6 + 1 ) X 1
= 39 years
4) Rule :
If one person come in any group and average age of group decrease then age of new person.
= before average - new number X decrease average age
Example :
Average age of 20 teachers are 45 years after joining one student the average age of group is decrease by 6/7. What was the student age ?
Sol.
Student's age = before average - new number X decrease average age
= 45 - (20+1 ) X 6/7
= 27
5) Rule :
If one person out any group and average age of group increase then age of new person.
= before average - new number X increase average age
Example :
Average age of 10 girls are 19 years . If Mamta left the group , average age of group is increase 1/2 year then age of Mamta .
Sol.
Mamta's age = before average - new number X increase average age
= 19 - (10 - 1 ) X 1/2
= 14.5 years
6) Rule :
If one person out any group and average age of group decrease then age of new person.
= before average + new number X decrease average age
Example :
Average age of 26 boys are 30 years . If Manoj left the group , average age of group is decrease 1/5 year then age of Manoj .
Sol.
Manoj's age = before average + new number X decrease average age
= 30 + (26 -1 ) X 1/5
= 35 years
7) Rule :
If ratio of father and son is x : y after t years it will a : b then
t (a-b )
Son's age = y X--------------------
xb - ya
t (a-b )
Father's age = x X------------------
xb - ya
Example :
If ratio of father and son is 6 : 1 . After 5 years it will be 7 : 2 then what will be age of father and son .
Sol.
5 (7-2 )
Son's age = 1 X-----------------
6 X 2 -7 X 1
= 5 years
5( 7 - 2 )
Father's age = 6 X ----------------
6 X 2 - 7 X 1
= 30 years
8) Rule :
If ratio of father and son is x : y , t years ago it was a : b then
t (a-b )
Son's age = y X--------------------
xb - ya
t (a-b )
Father's age = x X------------------
xb - ya
Example :
If ratio of father and son is 3 : 1 . 4 ago years it was be 4 : 1 then what was the age of father and son .
Sol.
4 (4 - 1 )
Son's age = 1 X-------------------
4 X 1 - 3 X 1
= 12 years
4 ( 4 -1 )
Father's age = 3 X ---------------------
4 X 1 - 3 X 1
= 36 years.
9) Rule :
t years ago father age x time of his son age . Present age of father y time of his son age ,then
t ( x - 1 )
Son's age = ----------------
x - y
Example :
Five years ago father's age 4 time of his son . Present age of father is 3 time of his son's age , then
5 ( 4 - 1 )
Son's age = ------------------- = 15 years
4 - 3
Father's age = 15 X 3 = 45 years
10) Rule :
Present age of father is y time of his son age . After t years father's age z time of his son age . Find present age of father and son .
t ( z - 1 )
Son's age = -------------------
y - z
Example :
At present age of father is 4 time of his son , after 5 years father's age will be 3 time of his son's age .Find the present age of father and son ?
Sol.
5 ( 3 - 1 )
Son's age = ------------------- = 10 years
4 - 3
Father's age = 10 X 3 = 30 years
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Exercise
1) Two years ago a man was 6 times as old as his son . In 18 years , he will be twice as old as his son . Their present ages are :
a) 32 years , 7 years b) 34 years , 9 years c) 36 years , 11 years d)None of these
2) The ages of two persons differ by 20 years. If 5 years ago , the elder one be 5 times as old as the younger one , their present ages are :
a) 30 years , 10 years b) 25 years , 5 years c) 29 years , 9 years d) 50 years , 30 years
3)One year ago the ratio of Varun and Veena's age was 4 : 5 . One year hence the ratio of their ages will be 5 : 6 . The present age of Veena is :
a) 9 years b)10 years c) 12 years d) 6 years
4)10 years ago , Mona's mother was 4 times older than her daughter . After 10 years , the mother will be twice older than the daughter . Mona's present age is :
a) 5 years b) 10 years c) 20 years d) 30 years
5) A is as much younger to B as he is older to C . If the sum of the ages of B and C is 48 years , what is the present age of A ?
a) 20 years b) 24 years c) 30 years d) 36 years
Answer :
1) a 2) a 3) c 4) c 5) b
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