Multiple choice

If Ajit can do $\displaystyle \frac{1}{4}$ of the works in $3$ days and Sujit can do $\displaystyle \frac{1}{6}$ of the same work in $3$ days, how much will Ajit get if both work together and are paid Rs. $180$ in all?

  1. Rs. $120$
  2. Rs. $108$
  3. Rs. $60$
  4. Rs. $36$
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A Correct answer
AI explanation

Using the unitary method to find the work rates, Ajit completes 1/4 of the work in 3 days, so his daily work rate is 1/12. Sujit completes 1/6 of the work in 3 days, so his daily work rate is 1/18. The ratio of their efficiencies is 1/12 to 1/18, which is equivalent to 3 to 2. Ajit's share of the total Rs. 180 is 3 divided by the sum of the ratio parts, 3 plus 2, times 180. This calculates to 3/5 times 180, which equals Rs. 120.

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