Time and Work Fractional Day – UGC NET Question

A’s one-day work is 1/15 of the job and B’s one-day work is 1/20 of the job. Their combined daily work is 1/15 + 1/20. The least common multiple of 15 and 20 is 60, so this becomes 4/60 + 3/60 = 7/60 of the work per day. The total time to complete one whole work is therefore 1 ÷ (7/60) = 60/7 ≈ 8.57 days. Among the integer options given, 9 days is the closest approximation to 60/7, so it is the most appropriate answer.

Option A:
Option A, 8 days, underestimates the exact value of about 8.57 days; in 8 days they would complete only 8 × 7/60 = 56/60 of the work, leaving some part unfinished.

Option B:
Option B, 9 days, is the nearest whole number to 60/7 and slightly overestimates the exact time, which is why it is the best choice among the given options.

Option C:
Option C, 10 days, deviates further from the exact value and would correspond to a slower combined rate than actually calculated.

Option D:
Option D, 12 days, is much larger than 60/7 and ignores the productivity gain from having both A and B work together.