GRE® Quant Practice | Rates Q1

The GRE maths sample question given below is a work and time question in Rates. This GRE sample question help you to understand the relation between Work done and time taken to complete the work.

Question 1: A and B together complete a work in 4 days, B and C together in 6 days, C and A together in 5 days. Working independently, who will finish the work in the least time and in how many days ?

1. A, \\frac{120}{7}) days
2. A, \\frac{120}{17}) days
3. B, \\frac{120}{13}) days
4. B, \\frac{120}{17}) days
5. C, \\frac{120}{7}) days

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Video Explanation

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Explanatory Answer | GRE Rates Practice Q1

Given Data: Work done by A, B, and C

Let the fraction of work done by A, B, and C in a day be a, b, and c respectively.
A and B complete the work in 4 days.
Fraction of work done by A and B together in 1 day → a + b = \\frac{1}{4}) ------(1)
B and C complete the work in 6 days.
Fraction of work done by B and C together in 1 day → b + c = \\frac{1}{6}) ------(2)
C and A complete the work in 5 days.
Fraction of work done by C and A together in 1 day → c + a = \\frac{1}{5}) ------(3)

Step 1 of solving this GRE Work & Time Question: Solving equations for a, b, and c

Add (1), (2), and (3)
2a + 2b + 2c = \\frac{1}{4}) + \\frac{1}{6}) + \\frac{1}{5})
Take LCM (4, 6, 5) = 60
2 (a + b + c) = \\frac{15 + 10 + 12}{60})
a + b + c = \\frac{37}{120}) ------(4)

Subtract (1) from (4), we get
c = \\frac{37}{120}) - \\frac{1}{4})
c = \\frac{37 - 30}{120}) → c = \\frac{7}{120})

Substitute c = \\frac{7}{120}) in (2), we get
b = \\frac{1}{6}) - \\frac{7}{120}) = \\frac{20 - 7}{120})
b = \\frac{13}{120})

Substitute c = \\frac{7}{120}) in (3), we get
a = \\frac{1}{5}) - \\frac{7}{120}) = \\frac{24 − 7}{120})
a = \\frac{17}{120})

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Step 2 of solving this GRE Work & Time Question: Compute the least time taken

Solving for a, b, and c, we got
a = \\frac{17}{120}) ; b = \\frac{13}{120}) ; c = \\frac{7}{120})

Rate is inversely proportional to time.
Greater the value of work done, lesser the time taken
The rate at which a completes the work is the greatest among the three.
So, A would finish the work in the least time and in \\frac{120}{7})

Choice B is the correct answer