Question

Question :-
six years ago the ratio of ages of A&B was 1:3 and after six years the ratio becomes 2:3.find the sum of present age of A&B.​

Answer 1

Step-by-step explanation:

Given:

• Six years ago, the ratio of ages of A and B was 1:3.
• After six years, the ratio becomes 2:3.

To find:

• Sum of the present ages of A and B.

Solution:

Let the present ages of A and B be x and y years respectively.

Their ages 6 years ago will be : [Past]

• x - 6
• y - 6

According to the condition :

• Ratio becomes 1:3

Therefore :

• (x - 6)/(y - 6) = 1/3

Cross multiplication :

⇒ 3(x - 6) = y - 6

⇒ 3x - 18 = y - 6

⇒ 3x - y = -6 + 18

⇒ 3x - y = 12 - (1)

Their ages after 6 years will be : [Future]

• x + 6
• y + 6

According to the condition :

• Ratio becomes 2:3

Therefore :

• (x + 6)/(y + 6) = 2/3

Cross multiplication :

⇒ 3(x + 6) = 2(y + 6)

⇒ 3x + 18 = 2y + 12

⇒ 3x - 2y = 12 - 18

⇒ 3x - 2y = -6 - (2)

Subtracting (2) from (1) :

⇒ 3x - y = 12

⇒ 3x - (+) 2y = -6 (+)

• y = 18

Substituting value of y in (2) :

⇒ 3x - 2y = -6

⇒ 3x - 2(18) = -6

⇒ 3x - 36 = -6

⇒ 3x = -6 + 36

⇒ 3x = 30

⇒ x = 30/3

⇒ x = 10

So the ages of A and B are :

• A = 10 years
• B = 18 years

Sum of the ages is :

• A + B
• 10 + 18
• 28 years

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