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29 Feb 2020, 14:36
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
60% (03:15) correct
40%
(03:32)
wrong
based on 215
sessions
History
Date
Time
Result
Not Attempted Yet
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
29 Feb 2020, 23:29
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jackfr2
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
General Discussion
Archit3110
01 Mar 2020, 01:25
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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
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
jackfr2
