Question 11 of 49intermediate🔧 ApplyNumerical3 marks

The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Correct Answer

Let Salil's present age be x years. Since his mother's present age is three times his, her age is 3x years.

After 5 years, Salil's age will be (x + 5) years and his mother's age will be (3x + 5) years. According to the question, the sum of their ages after 5 years is 70.

Step 1: Form the equation: (x + 5) + (3x + 5) = 70 Step 2: Simplify the equation: 4x + 10 = 70 Step 3: Solve for x: 4x = 60 => x = 15 Step 4: Find mother's age: 3x = 3 * 15 = 45 Thus, Salil's present age is 15 years and his mother's present age is 45 years.

Exercise: Exercise Set 2.2 | Q: 3 | (Page 6)
For More Understanding

Explanation

The problem is solved by forming a linear equation based on the given conditions. Letting Salil's age be x, his mother's age is 3x. The condition for their ages after 5 years gives the equation (x+5) + (3x+5) = 70, which simplifies to 4x + 10 = 70. Solving this yields x = 15, making the mother's age 45.

Solution Steps

  1. Step 1: Let Salil's present age be x years. Then his mother's present age is 3x years.

  2. Step 2: After 5 years, their ages will be (x + 5) and (3x + 5) respectively.

  3. Step 3: Form the equation: (x + 5) + (3x + 5) = 70

  4. Step 4: Simplify to get 4x + 10 = 70, which gives 4x = 60, so x = 15.

  5. Step 5: Calculate mother's age: 3x = 3(15) = 45.

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