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?

Explanation:-

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.

Short-cut method:
If there is a provision of food for A men for a days and after b days if B men join them or leave