Explanation
Given:
X:Y=3:4andY:Z=5:8
Step 1: Make Y common
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From X:Y=3:4, letX=3k, Y=4k
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From Y:Z=5:8, let Y=5m, Z=8m
Step 2: Equate Y
4k=5m⟹k=5/4m
Then:
X=3k=3⋅5/4m=15/4m
Y=4k=5mZ=8m
Step 3: Compute the expression
2Y/3X−Y+2Z=2⋅5m/ 3⋅15/4m−5m+2⋅8m
Numerator: 2⋅5m=10m
Denominator:
3⋅15/4m=45/4m
45/4m−5m+16m=45/4m−20/4m+64/4m=89/4m2Y/3X−Y+2Z=10m/89/4=10⋅4/89=40/89