A garrison of 140 men has provisions for 35 days. At the end of 10 days, 35 more men joined them. How many days can they sustain on the remaining provisions?

Given:

A garrison of 140 men has provisions for 35 days. At the end of 10 days, 35 more men joined them.

Formula used:

Initial total provisions = Number of men × Number of days

Remaining provisions after 10 days = Initial total provisions - (Number of men × Days consumed)

New number of men = Initial number of men + Additional men

New number of days = Remaining provisions / New number of men

Calculation:

Initial total provisions = 140 × 35

⇒ Initial total provisions = 4900 man-days

Days consumed = 10

Men during first 10 days = 140

Provisions consumed in first 10 days = 140 × 10

⇒ Provisions consumed in first 10 days = 1400 man-days

Remaining provisions = 4900 - 1400

⇒ Remaining provisions = 3500 man-days

New number of men = 140 + 35

⇒ New number of men = 175

New number of days = Remaining provisions / New number of men

⇒ New number of days = 3500 / 175

⇒ New number of days = 20

∴ The correct answer is option 2.