Five years ago, Nuri was thrice as old as Sonu. After ten years from now, Nuri will be twice as old as Sonu. Find the present ages of Nuri and Sonu, respectively.

Question

Accepted Answer

Let the present ages of Nuri and Sonu be $$ x $$ and $$ y $$, respectively.

### Step 1: Form equations based on the given conditions  
1. **Condition 1 (Five years ago):**  
   Five years ago, Nuri’s age was three times Sonu’s age:  
   $$
   x - 5 = 3(y - 5)
   $$  
   Simplify:  
   $$
   x - 5 = 3y - 15 \implies x - 3y = -10 	ag{1}
   $$

2. **Condition 2 (Ten years from now):**  
   Ten years from now, Nuri’s age will be twice Sonu’s age:  
   $$
   x + 10 = 2(y + 10)
   $$  
   Simplify:  
   $$
   x + 10 = 2y + 20 \implies x - 2y = 10 	ag{2}
   $$

### Step 2: Solve the equations  
From equations (1) and (2):  
1. Subtract equation (1) from equation (2):  
   $$
   (x - 2y) - (x - 3y) = 10 - (-10)
   $$  
   Simplify:  
   $$
   y = 20
   $$

2. Substitute $$ y = 20 $$ into equation (1):  
   $$
   x - 3(20) = -10
   $$  
   Simplify:  
   $$
   x - 60 = -10 \implies x = 50
   $$

### Final Answer:  
Nuri’s present age is $$ x = 50 $$ years, and Sonu’s present age is $$ y = 20 $$ years. Thus, the correct answer is **(d)**.

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