GRE® Quant Practice | Rates Q4

The GRE maths sample question given below is a work and time question in Rates. A medium difficulty GRE Numeric Entry practice question. This GRE sample question helps you understand the concept of framing equations for Work Time.

Question 4: If machine A polishes x units in 12 minutes and machine B polishes 5x units in 40 minutes, in how many minutes will A and B, working together, polish 50x units.

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Video Explanation

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Explanatory Answer | GRE Numeric Entry Practice Question 4

Given Data

Machine A polishes x units in 12 minutes.
So, in 1-minute, Machine A will polish \\frac{x}{12}) units.

Machine B polishes 5x units in 40 minutes
⇒ Machine B polishes x units in \\frac{40}{5}) = 8 minutes.
So, in 1-minute, Machine B will polish \\frac{x}{8}) units.

Compute Time taken by A & B together to polish 50x units

In 1-minute, Machine A and B, together, will polish \\frac{x}{12}) + \\frac{x}{8}) units
⇒ \\frac{(2 + 3)x}{24}) = \\frac{5x}{24}) units in 1 minute.

Cross multiplying, in 24 minutes the 2 machines, together, will polish 5x units.
Time taken to polish 50x units: The 2 machines will take 24 × 10 = 240 minutes.

240 minutes is the correct answer