Multiple choice

A, B and C can complete a work in x, 1.5x and 2x days, respectively. If they complete the work together, in what ratio should they be paid?

  1. 2 : 3 : 4

  2. 6 : 4 : 3

  3. 3 : 2 : 1

  4. 4 : 3 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done is inversely proportional to time taken. The ratio of times is x : 1.5x : 2x = 1 : 1.5 : 2 = 2 : 3 : 4. The ratio of work (and pay) is the reciprocal: 1/2 : 1/3 : 1/4 = 6 : 4 : 3.

AI explanation

The wages of A, B and C will be in the ratio of the work they do per day. Their one day's work is 1/x, 1/(1.5x) and 1/(2x) respectively. Converting these fractions to a ratio gives (1/x) : (2/3x) : (1/2x), which simplifies to 1 : 2/3 : 1/2. Multiplying by the lowest common multiple of 6 yields the ratio 6 : 4 : 3.

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