James hired some workers to build his house in 20 days. But on the day of starting of the construction, 12 men did not come. Rest of the people then built the entire house in 32 days. How many workers had he initially hired?

Question: James hired some workers to build his house in 20 days. But on the day of starting of the construction, 12 men did not come. Rest of the people then built the entire house in 32 days. How many workers had he initially hired?

Solution:
Initially hired workers = x
Total work = x × 20 (man-days)
After 12 workers didn't come, Remaining workers = x - 12
Total work = (x - 12) × 32 (man-days)

ATQ,
x × 20 = (x - 12) × 32
⇒ 20x = 32x - 384
⇒ 12x = 384
∴ x = 32