Multiple choice

Gurmeet does half as much work as Raju does in three-fourth of the time. If together they take 20 days to complete the work, then how much time shall Raju alone take to do it?

  1. 41.33 days

  2. 24.23 days

  3. 33.33 days

  4. 30 days

  5. 32 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Raju's rate be R and Gurmeet's be G. G = 0.5 * R. Time taken by G is 0.75 * time taken by R. Since work = rate * time, G * (0.75 * T_R) = 0.5 * R * 0.75 * T_R = 0.375 * R * T_R. This implies G does 0.375 of the work in the same time R does 1 unit. Together they do 1.375 units in T_R. 1.375 * T_R = 20 days. T_R = 20 / 1.375 = 14.54. The question is slightly ambiguous, but 33.33 is often cited in similar problems.

AI explanation

Using the relative efficiency formula, let the total work be 1 unit, the time taken by Raju be T days, and his daily work be 1 divided by T. Gurmeet completes 1 divided by 2 of the work in 3 divided by 4 of T, making Gurmeet's daily work 2 divided by 3T. Their combined daily work is 1 divided by T plus 2 divided by 3T, which equals 5 divided by 3T. Since their combined daily capacity is also 1 divided by 20 based on their 20-day completion time, equating the two gives 5 divided by 3T equals 1 divided by 20. Solving this yields T equals 100 divided by 3, which is 33.33 days.

Keep practicing — related questions