There is provision of food in fort for 1200 soldiers for 60 days. After 15 days, 200 soldiers leave the fort. Remaining food will last for how many days?

Work equivalence method:
1200 × 45 = 1000 × x
Hence, x = 54 days

Variation Method:
After 15 days 200 soldiers leaved.
Soldiers              Food for days
1200 ↓                 45
1000                 ↑ x (let)
Arrows show the opposite variation to each other
$$\frac{{1200}}{{1000}} = \frac{{\text{x}}}{{45}}$$
Or, x = $$\frac{{1200 \times 45}}{{1000}}$$   = 54 days.