I am solving the following question. Please guide me!!
The ages of A and B are in the ratio of 5:7 and C and D are in the ratio of 5:7.Let sum of their ages is 150, what is the difference between the ages of A and D?
My Solution:
$A/B= 5/7$ , Thus $B=7A/5$
$C/D= 5/7$ , Thus $C=5D/7$
As sum is 150, we can write
$A + B + C + D= 150$
$A + (7A/5) + (5D/7) + D = 150$
$(12A/5) + (12D/7) =150$
$A/5 + D/7 = 150/12$
$A/5 + D/7 = 12.5$
Now how to find difference between ages of A and D now? Is my way of solving question wrong.
Thankyou in advance
If we assume the ages of A and B to be 5x and 7x, respectively, and those of C and D to be 5y and 7y, respectively, we get
12x + 12y = 150 which gives x + y = 12.5
Now, unless x and y are equal, which we can't assume, it's not possible to find the difference between ages of A and D. (5x and 7y)
So, to summarise, you have one equation and two unknown parameters. It's not possible to deduce them uniquely.