1. **State the problem:** Abdullah gave 60 to Umar, and Umar gave 90 to Ahmed. After these transactions, all three have the same amount of money. We need to find how much more Umar has than Ahmed. 2. **Define variables:** Let the initial amounts of money Abdullah, Umar, and Ahmed have be $A$, $U$, and $H$ respectively. 3. **Write equations after transactions:** - Abdullah gives 60 to Umar: Abdullah now has $A - 60$, Umar has $U + 60$. - Umar gives 90 to Ahmed: Umar now has $(U + 60) - 90 = U - 30$, Ahmed has $H + 90$. 4. **Since all have the same amount after transactions:** $$A - 60 = U - 30 = H + 90 = M$$ where $M$ is the common amount each has after transactions. 5. **Express initial amounts in terms of $M$:** - From $A - 60 = M$, we get $A = M + 60$. - From $U - 30 = M$, we get $U = M + 30$. - From $H + 90 = M$, we get $H = M - 90$. 6. **Find how much more Umar has than Ahmed initially:** $$U - H = (M + 30) - (M - 90) = 30 + 90 = 120$$ **Final answer:** Umar initially has 120 more than Ahmed.