# GRE® Quant Practice | Rates Q1

#### GRE Sample Questions | Work Time

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, $$frac{120}{7}$ days 2. A, $\frac{120}{17}$ days 3. B, $\frac{120}{13}$ days 4. B, $\frac{120}{17}$ days 5. C, $\frac{120}{7}$ days ## Get to 170 in GRE Quant #### Online GRE Courses From INR 2999 ### Video Explanation ## GRE Live Online Classes #### Starts Fri, August 26, 2022 ### Explanatory Answer | GRE Rates Practice Q1 #### Given Data: Work done by A, B, and C Let the fraction of work done by A, B, and C in a day be a, b, and c respectively. A and B complete the work in 4 days. Fraction of work done by A and B together in 1 day → a + b = $\frac{1}{4}$ ------$1)
B and C complete the work in 6 days.
Fraction of work done by B and C together in 1 day → b + c = $$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

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)
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