There are five members i. a family named a,b,c,d,e. Ratio of ages of b to e is 3:1. After one year, the age of c will become twice the age of e. After 2 years, the ratio of ages of a,d and e is 4:2:1. If the present average age of five members is 18.6 years, Find the sum of the ages of a and b?
Answers
The sum of the ages of a and b is 55 years
Given:
There are five members in a family named a,b,c,d,e.
Ratio of ages of b to e is 3:1
After one year, the age of c will become twice the age of e
After 2 years, the ratio of ages of a,d and e is 4:2:1
The present average age of five members is 18.6 years
To Find:
The sum of the ages of a and b
Solution:
Assuming ages of a , b c , d and e as a , b , c , d , e respectively.
Average of present ages = (a + b + c + d + e)/5 = 18.6
=> a + b + c + d + e = 93
Ratio of ages of b to e is 3:1
=> b = 3e
After one year, the age of c will become twice the age of e
=> c + 1 = 2(e + 1)
=> c = 2e + 1
After 2 years, the ratio of ages of a,d and e is 4:2:1.
=> (a + 2) : (d + 2) : (e+2) ::: 4:2:1.
=> a + 2 = 4(e + 2)
=> a = 4e + 6
=> d + 2 = 2(e + 2)
=>d = 2e + 2
Substituting a , b , c , d values in terms of e in a + b + c + d + e = 93
4e + 6 + 3e + 2e+1 + 2e + 2 + e = 93
=> 12e + 9 = 93
=> 12e = 84
=> e = 7
a = 4e + 6 = 4(7) + 6 = 34
b = 3e = 3(7) = 21
c = 2e+ 1 = 2(7) + 1 = 15
d = 2e+ 2 = 2(7) + 2 = 16
e = 7
the sum of the ages of a and b = 34 + 21 = 55
The sum of the ages of a and b is 55 years