Question

two years ago Saleem was thrice old as his daughter and six years later he will be four years older than twice her age. how old are they now​

Answer 1

❍ Let the present age of saleem be x years and his daughter be y years respectively.

Two years ago,

• Saleem's age = x - 2 years
• His daughter age = y - 2 years

$\\ \underline{\bigstar\boldsymbol{According \: to \: the \: given \: condition:}}$

• Saleem was thrice old as his daughter = 3(y - 2)years

$\\ \implies\sf{x - 2 = 3(y - 2)} \\ \\ \implies\sf{x - 2 = 3y - 6} \\ \\ \implies\sf{x - 3y = - 6 + 2} \\ \\ \implies\sf{x - 3y = - 4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashrightarrow \: \sf{eq(1)}$

Six years later,

• Saleem's age = x + 6 years
• His daughter age = y + 6 years
• Saleem will be 4 years older than twice her age = 2(y + 6) + 4

Then,

$\\ \implies\sf{x + 6 = 2(y + 6) + 4} \\ \\ \implies\sf{x + 6 = 2y + 12 + 4} \\ \\ \implies\sf{x + 6 = 2y + 16} \\ \\ \implies\sf{x = 2y + 16 - 6} \\ \\ \implies\sf{x - 2y = 10} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashrightarrow \: \sf{ eq(2)}$

Now,Substituting the eq(2) and eq(1),we get:

$\sf{ \cancel{x} - 2y = 10} \\ \\ \sf{ - \cancel{x} - 3y = - 4} \\ \\ - - - - - - - \\ \sf{ + \: 3y = 14} \\ \sf{ y = 14} \\ - - - - - - -$

• Therefore, value of y is 14

Putting the value of y in eq(2),

$\\ \dashrightarrow\sf{x - 2y = 10} \\ \\ \dashrightarrow\sf{x - 2(14) = 10} \\ \\ \dashrightarrow\sf{x - 28 = 10} \\ \\ \dashrightarrow\sf{x = 10 + 28} \\ \\ \dashrightarrow \: \underline{ \boxed{\frak{x = 38}}} \: \red{ \bigstar}$

Hence,

• Saleem age = 38 years
• His daughter age = 14 years

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