Question

25. If age of P and R are added to twice the age of Q, the total

becomes 59. It the ages of Q and R are added to thrice

the age of P, the total become 68. And if the age of P is

added to thrice the age of Q and thrice age of R, the total

becomes 108, what is the total of ages of P, Q and R ?

Answer 1

eq. 1:- P+R+2Q=59
eq. 2:- Q+R+3P=68
eq. 3:- P+3Q+3R=108
So,
=>from eq 1
we got (R+Q)+Q=59-P

=>from eq 2
we got Q+R=68-3P

=>from eq 3
we got Q+R=(108-P)/3

Since Q+R=Q+R
68-3P=(108-P)/3
=>204-9P=108-P
=>8P=204-108
=>8P=96
So, P=12
So, Q+R=68-36=32
putting this in eq 1,
(R+Q)+Q=59-P
=>32+Q=59-12
=>Q=47-32=15
So,R=32-15=17