10 women can complete a work in 7 days and 10 children take 14 days to complete the same work. How many days will 5 women and 10 children take to complete the work?

Work and time problems become easy once you convert everyone into a common unit. Let the total work be W. Then 10 women in 7 days means one woman does W/70 per day, so 1 woman equals 2 children, since 10 children in 14 days means one child does W/140 per day.

Now take 5 women and 10 children together. Their daily rate is 5(W/70) + 10(W/140) = W/14 + W/14 = W/7. So the work finishes in 7 days. Option D is correct.

• A) 3 and B) 4: These would need a combined daily rate of W/3 or W/4, which is more than the group can do. Five women alone take 14 days, and 10 children alone take 14 days, so the combined group must be slower than 7 days only if rates are added wrongly. Both answers come from treating people as if they were all equally efficient.
• C) 5: This comes from simply adding the given figures or averaging the days (7 and 14 give 10.5, and similar shortcuts give 5), without converting women to children or working with rates.

The core concept is work equals rate multiplied by time, with rates added across workers. This sits squarely in the quantitative aptitude and work-time portion of the syllabus, and the same unit-conversion habit helps in data interpretation.

Trap: Aspirants add the days or average them instead of adding the daily work rates.