Question

plzz help me in solving this question. 4 years ago the ratio of ages of A and B was 2:3 and after four years it becomes 5:7. find their present ages.

Answer 1

Let the age of A 4 years ago = 2x.

Let the age of B 4 years ago = 3x.

Their present ages:

Age of A = 2x + 4.

Age of B = 3x + 4.

Now,

Given that after 4 years it becomes 5:7.

= > (2x + 4) + 4/(3x + 4) + 4 = 5/7

= > (2x + 8)/(3x + 8) = 5/7

= > 7(2x + 8) = 5(3x + 8)

= > 14x + 56 = 15x + 40

= > -x = -16

= > x = 16.

Then,

Present age of A = 2(16) + 4

= > 32 + 4

= > 36.

Present age of B = 3x + 4

= > 3(16) + 4

= > 52.

Hope this helps!

Answer 2

Define x:

Four years ago, the ratio of A : B = 2 : 3

Let x be the constant ratio

ratio of A : B = 2x : 3x

Express their current age in term of x:

A = 2x + 4

B = 3x + 4

Express their age 4 years later:

A = 2x + 4 + 4 = 2x + 8

B = 3x + 4 + 4 = 3x + 8

Form equation and solve for x:

Their ratio 4 years later is  5: 7

(2x + 8) / (3x + 8) = 5/7

7(2x + 8) = 5(3x + 8)

14x + 56 = 15x + 40

x = 16

Find their present age:

A = 2x + 4 = 2(16) + 4 = 36

B = 3x + 4 = 3(16) + 4 = 52

Answer: A is 36 years old and B is 52 years old