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Re: Rufus has a total of 20 coins of 2 types, Type Q and Type R. The value
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16 Feb 2024, 22:52
Solution
We have twenty coins => Q+R = 20
The italics Q and R make this a bit problematic in reading.
So let us take X=P and Y=R. => X+Y=130
The options given are for X and Y.
The total amount is 130, where each Q=5q and each R=5r => Q*5q+R*5r = 130
Let us use the options.
We can clearly see there are three set of options totalling to 130: (25,105), (60,70) and (65,65).
Let us write down the factors of options and see if Q +R comes out to be 20.
1. (25,105)
25 => 1,5,25
105 => 1,3,5,7,15,35,105
Factors (Q and R) that add up to 20 are (5,15)
So, 15*5q+5*5r=130….25(3q+r)=130
No integer values possible for q and r
2. (60,70)
60 => 1,2,3,4,5,6,10,12,15,20,30,60
70 => 1,5,7,10,14,70
Factors that add up to 20 are (15,5) and (14,6)
We know (15,5) does not fit in.
So, 14*5q+6*5r=130………10(7q+3r)=130……..7q+3r=13
q=1 and r=2 is the solution of above equation.
Q>R, so Q=14 and R=6
14*5+6*(5*2)=70+60=130
Thus X=14*5=70 and Y=6*10=60.