Question

Five years age, sunny was three times as old as minu.10years later,sunny would be twice as old as minu. How old are they now.

Answer 1

GIVEN:

• Five years ago, sunny was three times as old as Minu.
• 10 years later,Sunny would be twice as old as Minu

TO FIND:

• Find their present ages ?

SOLUTION:

Let the present age of Sunny be 'x' years and that of Mini be 'y' years

CASE:- 1

Five years ago, sunny was three times as old as minu.

• Sunny's age = (x–5) years
• Minu's age = (y–5) years

$\rm{\dashrightarrow (x-5) = 3(y -5)}$

$\rm{\dashrightarrow x -5 = 3y - 15}$

$\rm{\dashrightarrow x - 3y = -15 +5}$

$\bf{\dashrightarrow x - 3y = -10....1)}$

CASE:- 2

10 years later,Sunny would be twice as old as Minu

• Sunny's age = (x + 10) years
• Minu's age = (y + 10) years

$\rm{\dashrightarrow (x +10) = 2(y+10) }$

$\rm{\dashrightarrow x + 10 = 2y + 20}$

$\rm{\dashrightarrow x = 2y + 20-10}$

$\bf{\dashrightarrow x = 2y + 10....2)}$

Put the value of 'x' from equation 2) in equation 1)

$\rm{\dashrightarrow (2y +10) -3y = -10 }$

$\rm{\dashrightarrow 2y +10-3y = -10 }$

$\rm{\dashrightarrow 2y - 3y = -10-10 }$

$\rm{\dashrightarrow -y = -20 }$

$\bf{\dashrightarrow y = 20 }$

Put the value of 'y' in equation 2)

$\rm{\dashrightarrow x = 2 \times 20 + 10}$

$\rm{\dashrightarrow x = 40 + 10 }$

$\bf{\dashrightarrow x = 50}$

• Sunny's age = x = 50 years
• Minu's age = y = 20 years

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