NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.3
Question 16

Question. 16

Two years ago, Salim was thrice his daughter's age. Six years later, he will be four years older than twice her age. Find their present ages.

Salim: \(38\) years; Daughter: \(14\) years.

Step 1: Assume present ages.

Let Salim's present age be \(S\) years.

Let his daughter's present age be \(D\) years.

Step 2: Write the first condition.

Two years ago, Salim was thrice his daughter's age.

That means:

\(S - 2 = 3(D - 2)\)

Simplify:

\(S - 2 = 3D - 6\)

\(S = 3D - 4\) … (1)

Step 3: Write the second condition.

Six years later, Salim will be four years older than twice her age.

That means:

\(S + 6 = 2(D + 6) + 4\)

Simplify:

\(S + 6 = 2D + 12 + 4\)

\(S + 6 = 2D + 16\)

\(S = 2D + 10\) … (2)

Step 4: Solve the two equations.

From (1): \(S = 3D - 4\)

From (2): \(S = 2D + 10\)

Equating them:

\(3D - 4 = 2D + 10\)

\(3D - 2D = 10 + 4\)

\(D = 14\)

Step 5: Find Salim's age.

Put \(D = 14\) in (1):

\(S = 3(14) - 4\)

\(S = 42 - 4\)

\(S = 38\)

Final Answer:

Salim is 38 years old and his daughter is 14 years old.