Question

Age of A is five years more than that of B 5 years ago the ratio of their ages was three is to 2

Answer 1

Age of A is 5 years more than that of B. 5 years ago the ratio of their ages was three is to two. Find their present ages.

Let B's age be x. It is given that the age of A is x + 5.

Then, it is also given that 5 years ago the ratio of their ages was in the ratio 3:2.

This means that:

Age of A = x, Age of B = x - 5.

Writing in the form of an expression:

• x/(x-5)=3/2

Doing cross multiplication:

• 2x = 3(x-5)
• 2x = 3x - 15
• 2x - 3x = -15
• -x -15
• x = 15

Therefore, present age of A is 20 (15+5) and present age of B is 15.

Answer 2

Solution

Given :-

• Age of A is five years more than that of B
• 5 years ago the ratio of their ages was 3 is to 2

Find :-

• Age of A & B

Explanation

Let,

• Age of A be = x years
• Age if B be ✓ y years

Case 1.

(Age of A is five years more than that of B)

==> x = 5 + y

==> x - y = 5__________(1)

Again

Case 2.

(5 years ago the ratio of their ages was 3 is to 2)

==> (x - 5):(y-5) = 3:2

==> (x -5)/(y-5) = 3/2

==> 2×(x-5) = 3×(y-5)

==> 2x - 10 = 3y - 15

==> 2x - 3y = -15 + 10

==> 2x - 3y = -5__________(2)

multiply by 2 in equ(1)

==> 2x - 2y = 10___________(3)

Subtract equ(2) & equ(3)

==> -3y + 2y = -5 - 10

==> -y = -15

==> y = 15

Keep in equ(3)

==> 2x - 2×15 = 10

==> 2x = 10 + 30

==> 2x = 40

==> 2x = 40

==> x = 40/2

==> x = 20

Hence

• Age of A will be = 20 years
• Age of B will be = 15 years .

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