Mark told John, "If you give me half your money, I will have Rs. 75." John…

Concept: A word problem that ties two unknown quantities together with two separate conditions translates into a system of two linear equations in two variables; solving that system (by substitution or elimination) gives the values of both unknowns.

Application:

1. Let Mark's money = M and John's money = J.

2. First condition — if John gives Mark half of John's money, Mark will have Rs. 75: M + J/2 = 75.

3. Second condition — if Mark gives John one-third of Mark's money, John will have Rs. 75: J + M/3 = 75.

4. From the first equation, M = 75 − J/2.

5. Substitute this into the second equation: J + (75 − J/2)/3 = 75.

6. Simplify: J + 25 − J/6 = 75, so 5J/6 = 50, giving J = 60.

7. Back-substitute to get M = 75 − 30 = 45.

Cross-check: With M = 45 and J = 60, Mark's share becomes 45 + 30 = 75 (half of John's 60), and John's share becomes 60 + 15 = 75 (one-third of Mark's 45) — both conditions hold.

Result: John had Rs. 60.