UGC-NET-Paper1

Let:
- The age of the father = F
- The age of the elder son = E
- The age of the younger son = Y

### Step 1: Form Equations
1st condition: "The age of the father is twice that of the elder son."
=> F = 2E ----(1)

2nd condition: "Ten years hence, the age of the father will be three times the age of the younger son."
=> (F + 10) = 3(Y + 10)
=> F + 10 = 3Y + 30
=> F = 3Y + 20 ----(2)

3rd condition: "The difference in the ages of the two sons is 15 years."
=> E - Y = 15 ----(3)

### Step 2: Solve for F
From equation (3):
=> E = Y + 15

Substituting this into equation (1):
=> F = 2(Y + 15)
=> F = 2Y + 30 ----(4)

Equating equation (2) and equation (4):
2Y + 30 = 3Y + 20
=> 30 - 20 = 3Y - 2Y
=> 10 = Y
=> Y = 10

### Step 3: Find F
Substituting Y = 10 in equation (4):

F = 2(10) + 30
=> F = 20 + 30
=> F = 50

Thus, the age of the father is **50 years**.

Answer: **(1) 50 years**