Question

If the ages of a and c are added to twice the age of b, the total becomes 59. if the ages of b and c are added to thrice the age of a, the total becomes 68. and if the age of a is added to thrice the age of b and thrice the age of c, the total becomes 108. what is the age of a? (a) 17 years (b) 19 years (c) 11 years (d) 12 years (e) 24 years

Answer 1

Let the “P”, “Q” and “R” are the ages of P, Q and R respectively.  Given that                                                         P +  2Q +  R = 59     ---------------  (1)                             3P +    Q +  R = 68     ---------------  (2)                               P +  3Q +3R = 108   ---------------  (3)To get the age of P, here, just two equations – (2) and (3) are sufficient. When we multiply equation (2) by 3, and subtract equation (3) from it, we get
                             9P +  3Q + 3R = 204     --------------- (2)                               P +  3Q + 3R = 108     --------------- (3)                             -     -        -          -                     --------------------------------------------------------                             8P                   =   96
                                   P  = 12 years Ans.

If this is not clear, please refer to the attached solution.
Even, as I suspect that this solution would not be much compatable with a android device, I m attaching the exact copy of this answer too ;)

Hope This Helps :)

Answer 2

Answer:

12 years

Step-by-step explanation:

Let the age of a be a

Let the age of b be b

Let the age of c be c

Now we are given that the ages of a and c are added to twice the age of b, the total becomes 59.

$\Rightarrow a+c+2b=59$   -1

Now we are given that the ages of b and c are added to thrice the age of a, the total becomes 68.

$\Rightarrow b+c+3a=68$  ----2

Now we are given that the age of a is added to thrice the age of b and thrice the age of c the total becomes 108

$\Rightarrow a+3b+3c = 108$  ---3

Solving 1 ,2 and 3

a= 12,b = 15 , c= 17

Hence the age of a is 12 years