Question

Five years ago, the ratio of A's age and B's
age was 5:6. The ratio of their ages will be
7:8, after five years. What is the ratio of the A's
present age and the B's present age ?​

Answer 1

Answer:

The ratio of age of A and B = 6 : 7

Step-by-step explanation:

Given:

• Five years ago, the ratio of A's age and B's age was 5:6.
• The ratio of their ages will be 7:8, after five years.

To find:

• What is the ratio of the A's present age and the B's present age ?

Solution:

Present age be:

• A : B = x : y

5 years ago,

• A : B = 5 : 6
• (x - 5) : (y - 5) = 5 : 6

Cross multiplication.

• 6(x - 5) = 5(y - 5)
• 6x - 30 = 5y - 25
• 6x = 5y - 25 + 30
• 6x = 5y + 5
• x = (5y + 5)/6

5 years after,

• A : B = 7 : 8
• (x + 5) : (y + 5) = 7 : 8

Cross multiplication.

• 8(x + 5) = 7(y + 5)
• 8x + 40 = 7y + 35
• 8x = 7y + 35 - 40
• 8x = 7y - 5

Substituting x.

• 8(5y + 5)/6 = 7y - 5

Cross multiplication.

• 8(5y + 5) = 6(7y - 5)
• 40y + 40 = 42y - 30
• 40y - 42y = - 30 - 40
• -2y = - 70
• y = 35

Finding x:

• x = (5y + 5)/6

Putting y.

• x = (5 × 35 + 5)/6
• x = (175 + 5)/6
• x = 180/6 = 30

Hence,

• A : B = x : y
• A : B = 30 : 35
• A : B = 6 : 7

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