Question

Three years ago, the ratio of the ages of A and B was 4:3.
Three years hence, the ratio of their ages will be 11:9. Find
the present ages of A and B

Answer 1

Question:

Three years ago, the ratio of the ages of A and B was 4:3. Three years hence, the ratio of their ages will be 11:9. Find the present ages of A and B.

Answer:

A's present age = 19 years

B's present age = 15 years

Solution:

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

Then , three years ago ;

A's age = (x-3) years

B's age = (y-3) years

Also, three years hence ;

A's age = (x+3) years

B's age = (y+3) years

According to the question;

Three years ago, the ratio of the ages of A and B was 4:3.

Thus;

=> (x-3):(y-3) = 4:3

=> (x-3)/(y-3) = 4/3

=> 3•(x-3) = 4•(y-3)

=> 3x - 9 = 4y - 12

=> 3x - 4y = 9 - 12

=> 3x - 4y = - 3 --------(1)

Also;

Three years hence, the ratio of ages of A and B will be 11:9.

Thus;

=> (x+3):(y+3) = 11:9

=> 9•(x+3) = 11•(y+3)

=> 9x + 27 = 11y + 33

=> 9x - 11y = 33 - 27

=> 9x - 11y = 6 ---------(2)

Now,

Multiplying both sides of eq-(1) , we get;

=> 3•(3x - 4y) = 3•(- 3)

=> 9x - 12y = - 9 ---------(3)

Now,

Subtracting eq-(3) from eq-(2) , we get;

=> (9x - 11y) - (9x - 12y) = 6 - (- 9)

=> 9x - 11y - 9x + 12y = 6 + 9

=> y = 15

Now,

Putting y = 15 in eq-(1) , we get;

=> 3x - 4y = - 3

=> 3x = 4y - 3

=> 3x = 4•15 - 3

=> 3x = 60 - 3

=> 3x = 57

=> x = 57/3

=> x = 19

Hence,

A's present age = x years = 19 years

B's present age = y years = 15 years

Answer 2

Given :-----

• 3 years ago, ratio A : B = 4:3
• 3 years Hence, ratio = 11:9 .

To Find :----

• Present age of A and B ?

__________________________________

→ Let Three years ago A age was = 4x years.

→ Let Three years ago B age was = 3x years .

So,

→ A present age = (4x+3) years .

→ B present age = (3x+3) years..

Now,

→ 3 years Hence, A will be = Present + 3 years = (4x+3)+3 = (4x+6) years .

→ 3 years Hence, B will be = Present + 3 years = (3x+3)+3 = (3x+6) years .

According To Question now,

→ (4x+6) : (3x+6) = 11 : 9

or,

→ (4x+6)/(3x+6) = 11/9

Cross - Multiply we get,

→ 36x + 54 = 33x + 66

→ 3x = 66-54 = 12

Dividing both sides by 3,

→ x = 4 .

Hence,

→ A age 3 years ago = 4x = 4*4 = 16 years .

→ B age 3 years ago = 3x = 3*4 = 12 years .

so,

→ A Present age = 16 + 3 = 19 years .

→ B present age = 12 + 3 = 15 years .

Hence, A is 19 years old and B is 15 years old.

______________________________________

Shortcut Trick to Solve Question :

⋆ 3 years ago Age⠀⠀➞ 3 Yrs.⠀⋆ Future Age

A : B⠀⠀⠀⠀⠀⠀⠀⠀⠀ A : B

⠀⠀4 : 3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 11 : 9

◗ Difference of both Ratios is (4 - 3) = 1 and, (11 - 9) = 2,

we will Multiply them by Opposite terms. Means by 3 in Present and By 2 in Future to make Difference Equal.

⠀⠀4 : 3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀11 : 9

× 2 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀× 1

_______________________________

⠀⠀8 : 6⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀11 : 9

Now, Difference Between Ratios are Same, i.e. (11 - 8) = (9 - 6) = 3.

So, we will find the Difference of Ratio in Ages, that Means we can find from like A 3 years before + 3 years Hence = 6 or, B (3+3) = 6 .

Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ 6 Years / 3

↦ 2

Now, Just Multiply the Outcome (2 in this Case) with any of the Ratio of find Age. Here we have to Find 3 years ago Age :

◗ A = (8 × 2) = 16 Years

◗ B = (6 × 2) = 12 Years

∴ Therefore, Present Age of A is = 16 + 3 = 19 Years

Present Age of B = 12 + 3 = 15 years ..

Hence, A is 19 years old and B is 15 years old ..

#BAL

#answerwithquality