12 men can complete half work in 12 days while 15 women can complete the full work in 24 days. Quantity-1 In how many days can 3 men and 5 women complete the same work . Quantity- 2 In how many days can 5 men and 2 women complete the same work.

First calculate individual work rates: 12 men do half work in 12 days, so 12 men do full work in 24 days, meaning 1 man takes 288 days. 15 women do full work in 24 days, so 1 woman takes 360 days. For Quantity I: 3 men + 5 women have rate 3/288 + 5/360 = 1/96 + 1/72 = 8/24 per day. For Quantity II: 5 men + 2 women have rate 5/288 + 2/360 = 5/288 + 1/180 = 7/24 per day. Since 8/24 > 7/24, Quantity I completes work faster, so Quantity I takes fewer days. Therefore Quantity I < Quantity II.