If (x+y) : (y+z) : (x+z) = 10 : 23 : 19 and x+y+z=13, then the value of z = ?

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29 Mar 2022 Ratio & Proportion

If (x+y) : (y+z) : (x+z) = 10 : 23 : 19 and x+y+z=13, then the value of z = ?

OPtion

1) 6
2) 3
3) 7
4) 5
5) 4
6) 8
7) 3.5
8) 4.5
9) 1.5
10) None of these

Solution

Let x+y=10x, y+z=23x, x+z=19x
Then, 2(x+y+z) = 10x+23x+19x = 52x
2*13 = 52x
x = 1/2
.'. x+y=10*(1/2)=5 --- (i)
y+z=23*(1/2)=23/2 ---(ii)
x+z=19*(1/2)=19/2 ---(iii)
Solving (i), (ii) & (iii), we get x=1.5, y=3.5, z=8

Correct Option: 6 Best Solution (1)