60 persons consume 300 kg of wheat in 40 days. In how many days will 25…

Concept

In constant-consumption problems, total quantity equals the number of persons multiplied by the number of days and by the consumption per person per day.

When every person consumes at the same rate, person-days per kilogram remains constant across equivalent situations.

Application

1. Let r be the wheat consumed by one person in one day. From the first situation, r = 300 ÷ (60 × 40) = 1/8 kg per person per day.

2. If 25 persons consume 100 kg in d days, then 25 × d × 1/8 = 100.

3. Therefore, 25d = 800, so d = 32 days.

Cross-check

In 32 days, 25 persons account for 25 × 32 = 800 person-days. At 1/8 kg per person per day, they consume 800 × 1/8 = 100 kg, which reproduces the required quantity.

Result

Therefore, 25 persons will consume 100 kg of wheat in 32 days.