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

Question 5: P and Q take 4 hours to complete a task. P, Q, and R take 2 hours to complete the task.

Quantity A | Quantity B |
---|---|

Time taken by P alone to complete the task. | Time taken by R alone to complete the task. |

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- Cannot be determined

From INR 2999

Let the time taken by P alone, Q alone, and R alone be p, q, and r hours respectively.

So, in 1 hour P will complete \\frac{1}{p})

So, in 1 hour Q will complete \\frac{1}{q})

So, in 1 hour R will complete \\frac{1}{r})

**Information 1**: P and Q complete the task in 4 hours.

Therefore, P and Q will complete \\frac{1}{4})^{th} of the task in 1 hour.

Fraction of work done by P and Q in 1 hour is \\frac{1}{p}) + \\frac{1}{q}) = \\frac{1}{4}) ..... (1)

P, Q, and R complete the task in 2 hours

Therefore, P, Q, and R will complete \\frac{1}{2}) the task in 1 hour.

Fraction of work done by P, Q, and R in 1 hour is \\frac{1}{p}) + \\frac{1}{q}) + \\frac{1}{r}) = \\frac{1}{2}) ..... (2)

**Subtract equation (1) from equation (2)**

\\frac{1}{p}) + \\frac{1}{q}) + \\frac{1}{r}) - \\frac{1}{p}) - \\frac{1}{q}) = \\frac{1}{2}) - \\frac{1}{4})

⇒ \\frac{1}{r}) = \\frac{1}{2}) - \\frac{1}{4})

So, r = 4

**R alone takes 4 hours.** to complete the task.

It is given that, P and Q together take 4 hours.

Therefore, each of P and Q alone will take more than 4 hours.

**Quantity A**: Time taken by P alone to complete the task. We know P takes more than 4 hours

**Quantity B**: Time taken by R alone to complete the task. R takes 4 hours to complete the task.

Quantity A > Quantity B

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