8 years ago, the ratio of A’s age to B’s age was 4:5. At present the

Question

8 years ago, the ratio of A’s age to B’s age was 4:5. At present the ratio of B’s age to C’s age is 4:5. At present, the difference between A’s age and C ‘s age is 20 years, then what is the sum of the ages of A, B and C?

A. 138 years
B. 122 years
C. 164 years
D. 148 years
E. 152 years

A. 138 years
B. 122 years
C. 164 years
D. 148 years
E. 152 years

GMATinsight · Accepted Answer

Current age of A = A
Current age of B = B = 4x
Current age of C = C = 5x

8 years ago, the ratio of A’s age to B’s age = (A-8)/(B-8) = 4:5

i.e. A's Age < B's Age

B:C = 4:5
i.e. if B = 4x then C = 5x

i.e. B's Age < C's Age

i.e. A < B < C

ALso, Difference of current ages of A and C = C-A = 20

i.e. A = C-20 = 5x-20

Now, using (A-8)/(B-8) = 4:5
i.e. 5A - 40 = 4B - 32
i.e. 5 (5x-20) - 4*(4x) = 40-32 = 8

i.e. 25x - 16x = 8+100 = 108
i.e. 9x = 108 
i.e. x = 12

sum of the ages of A, B and C = A+B+C = (5x-20) + 4x + 5x = 14x - 20 = 14*12 - 20 = 148

Answer: Option D

Archit3110 · Answer

need to notice the factor of age ∆ amongst a,b,c here
i.e c>b>a
so
a-8/b-8 = 4/5
b/c=4/5
c-a=20
solve in terms of a
5a-40=4b-32
5a-16/5*c= 8
25a-16c=40
25a-320-16a=40
a=40
then
200-4b=8
b=48
and 
c = 48*5/4 ; 60 
a+b+c = 40+48+60 ; 148
IMO D

AbhaGanu · Answer

Archit3110  how did you get 5a-40=4b-32?

Archit3110 · Answer

AbhaGanu 
I have just simplified the expression of the ratio...

AbhaGanu · Answer

Can you please elaborate? I'm unable to get it that way.  Archit3110

Posted from my mobile device

Archit3110 · Answer

AbhaGanu
question says 8 years ago, the ratio of A’s age to B’s age was 4:5
we can write it as : a-8/b-8 = 4/5 simplify this by cross multiplication we get 5a-40=4b-32 ---(1)

Later question says : At present the ratio of B’s age to C’s age is 4:5 i.e b/c=4/5 ---(2)

and At present, the difference between A’s age and C ‘s age is 20 years i.e c-a=20---(3)

Target what is the sum of the ages of A, B and C?

using 1,2 & 3 solve to get values of a,b,c
you can solve in terms of a
5a-40=4b-32
5a-16/5*c= 8
25a-16c=40
25a-320-16a=40
a=40
then
200-4b=8
b=48
and
c = 48*5/4 ; 60
a+b+c = 40+48+60 ; 148
IMO D

hope this helps

AbhaGanu

Can you please elaborate? I'm unable to get it that way. Archit3110

Posted from my mobile device

AbhaGanu · Answer

Hi  Archit3110  ! Thank you for the explanation. But I still haven't understood how has 5a-16/5*c= 8 arrived?

GMATinsight  How have you got i.e. 5 (5x-20) - 4*(4x) = 40-32 = 8?

GMATinsight · Answer

AbhaGanu Check the highlighted parts I just substituted teh values of A and B in the equation 5A - 40 = 4B - 32 i.e. 5A - 4B = 40 - 32 I hope this help!

ZulfiquarA · Answer

Current Age of B=4x
Current age of C=5x
Current Age of A=C-20 = 5x-20
Sum of their ages = 4x+5x+5x-20 = 14x-20=? 
Let's find x then, 
Ages 8 years ago = A/B=4/5 = 5x-20-8/4x-8=4/5 
After Solving x=12 
14x-20 = 14(12)-20 = 168-20=148  (D)

bumpbot · Answer

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8 years ago, the ratio of A’s age to B’s age was 4:5. At present the

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