The given question is a GMAT 575 to 625 level problem solving question testing concepts in Ratio & Proportion. This GMAT sample question tests the concept of sharing wages in proportion to the amount of work done. Time and Work Questions are often tested in the GMAT quant section and you have to master the process of forming equations when solving time and work problems.

Question 3 A, B, and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be C's share of the earnings?

- $1100
- $520
- $1080
- $1170
- $630

@ INR

** Concept: **The share of earnings that each receives will be in the ratio of the work done by them.

** Note: ** Ratio of work done and ratio of time taken to complete the task are inversely proportional.

Time taken by A, B, and C to complete the task are 6, 8, and 12 days respectively.

Ratio of time taken: A : B : C :: 6 : 8 : 12

As A takes 6 days to complete the job, if A works alone, A will be able to complete \{\frac {1} {6}}^{th}) of the work in a day.

Similarly, B will complete \{\frac {1} {8}}^{th}) and C will complete \{\frac {1} {12}}^{th}) of the work in one day.

Therefore, ratio of the work done by A : B : C :: \\frac {1} {6}) : \\frac {1} {8}) : \\frac {1} {12})

Ratio of share of earnings for A : B : C :: \\frac {1} {6}) : \\frac {1} {8}) : \\frac {1} {12})

Multiply all 3 ratios by a constant (k) will leave the ratio intact:

\\frac {1} {6}) : \\frac {1} {8}) : \\frac {1} {12}) = \\frac {k} {6}) : \\frac {k} {8}) : \\frac {k} {12})

Choose such a value for 'k' that the ratios that are now fractions can be converted into integers.

k should be a number that is divisible by all three numbers viz., 6, 8, and 12 so that the result is an integer.

'k' should therefore, be the LCM of 6, 8, and 12.

LCM of 6, 8, and 12 is 24. Substitute k = 24

Ratio of share of earnings = \\frac {24} {6}) : \\frac {24} {8}) : \\frac {24} {12}) = **4 : 3 : 2**

If A gets 4x, B will get 3x, and C will get 2x out of the total earnings of 9x.

**Total earnings: ** 9x = $2340

x = \\frac {2340} {9}) = $260

** C's share = 2x = $520**

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