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 ?

- A, \\frac{120}{7}) days
- A, \\frac{120}{17}) days
- B, \\frac{120}{13}) days
- B, \\frac{120}{17}) days
- C, \\frac{120}{7}) days

From INR 2999

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)**

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})**

Solving for a, b, and c, we got

a = \\frac{17}{120}) ; b = \\frac{13}{120}) ; c = \\frac{7}{120})

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,

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