Q.2 𝑥 ∶ 𝑦 ∶ 𝑧= 1/2:1/3:1/4.
What is the value of x+z-y/y ?
(A) 0.75
(B) 1.25
(C) 2.25
(D) 3.25
Problem Overview
The ratio x:y:z = 1/2 : 1/3 : 1/4 implies proportional values for x, y, and z. The task is to compute x + z – y/y, which evaluates to 1.25 among the given options.
Solving the Ratio
Ratios like x:y:z = 1/2 : 1/3 : 1/4 mean x, y, z are in proportion to these fractions. Find a common multiplier k such that:
- x = k/2
- y = k/3
- z = k/4
Substitute into Expression
x + z – y/y = [k/2 + k/4 – k/3]/ k3
Numerator simplifies to: k (1/2+1/4 -1/3) = k (6/12 + 3/12 – 4/12) = k 5×12
Dividing by y: (k x 5/12)/(k/3) = 5/12 x 3 = 5/4 = 1.25
SEO Article: Master Ratio Problems for CSIR NET
Master ratio problems in competitive exams like CSIR NET with this guide on solving x + z - y/y for the ratio x:y:z = 1/2:1/3:1/4. Fractions in ratios require proportional assignment to eliminate variables efficiently.
Quick Solution Recap
Assign x =k/2, \y = k/3,z = k/4. Plug in to get 5k/12/k/3 = 1.25. Verify options: only (B) fits.
Pro Tips
- LCD Method: LCD of denominators (12) confirms x:y:z = 6:4:3, then 6+3-4/4 = 1.25
- Common Error: Treating as product xyz =1/24 ignores ratio nature
