Question 521120

Let
Present age of Sister = s
Present age of Eldest brother = a
Present age of younger brother  = b
Present age of youngest brother = c



At present the sister's age is equal to the sum of her brothers' ages.
s=a+b+c...................(1)


Five years ago 
age of Eldest brother was = a-5
age of younger brother was = b-5
age of youngest brother was = c-5
Then
the sum of the brothers' ages was half the sister's present age
s/2=a-5+b-5+c-5
s/2=a+b+c-15
s =2(a+b+c-15).........(2)
Put the value of a+b+c from (1) to (2)
s = 2(s-15)
s=2s-30
s=30


And the eldest brother was 4 times as old as the youngest
a-5=4(c-5)
a-5=4c-20
a=4c-15.................(3)



Since their ages are equally spaced sum of ages of eldest brother and youngest brother divide by 2 will be equal to the age of younger brother 
b=(a+c)/2
2b=a+c...................(4)


Put the value of 's' and (a+c) in equation (1)
s=a+b+c
s=(a+c)+b
30=2b+b
30=3b
30/3=3b/3
10=b
b=10


Now again put the value of 'b' and 's' in equation (1)
30=a+10+c
30-10=a+c
20=a+c
20-c=a
a=20-c...........(5)


Put the value of 'a' from (5) to (3)
20-c=4c-15
-c-4c=-15-20
-5c=-35
-5c/-5=-35/-5
c=7
Put the value of 'c' in (3)
a=4c-15
a=4(7)-15
a=28-15
a=13



Present age of Sister = s = 30 years old
Present age of Eldest brother = a = 13 years old
Present age of younger brother  = b = 10 years old
Present age of youngest brother = c = 7 years old

Check
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13+10+7= 30 (which is present age of sister)


5 years back
============
age of Eldest brother was = a-5 = 13-5= 8
age of younger brother was = b-5 = 10- 5 = 5
age of youngest brother was = c-5 = 7-5 = 2

8+5+2 = 15 (which is half of the present age of sister)

And the eldest brother was 4 times as old as the youngest
Eldest brother was 8 which is 4 times of 2.