RP

Rahul Patel

2 months ago

Problems on Ages Mathematics Ratio

How do you solve a problem where the ratio of ages changes after a certain number of years?

I'm struggling with a specific type of age-related problem. In these questions, we're given the current ratio of two people's ages and told that after a certain number of years, their ages will be in a different ratio. How do we approach solving such problems systematically?

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AKB

Aarti Koushtubh Barad
2 months ago

To solve problems where the ratio of ages changes after a certain number of years, follow these steps:

  1. Let x and y be the current ages of the two people.
  2. Express the initial ratio: x:y = a:b (where a and b are given)
  3. Express the future ratio: (x+n):(y+n) = c:d (where n is the number of years and c and d are given)
  4. Set up the equation: x/y = a/b and (x+n)/(y+n) = c/d
  5. Cross multiply: dx + dn = cy + cn
  6. Substitute y = (b/a)x in the equation
  7. Solve for x
  8. Calculate y using the initial ratio

Example:
Current ratio of A's age to B's age is 5:7. After 8 years, it will be 3:4. Find their current ages.

Solution:
Let A's current age be 5x and B's current age be 7x
(5x + 8) : (7x + 8) = 3 : 4
4(5x + 8) = 3(7x + 8)
20x + 32 = 21x + 24
8 = x
A's current age = 5 × 8 = 40 years
B's current age = 7 × 8 = 56 years

Reference: IndiaBIX - Problems on Ages

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EA

Elias Agrawal
2 months ago

Thanks for the detailed explanation! This step-by-step approach is really helpful.
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JK

Jayshree Kalla
1 month ago

Could you provide another example with different ratios? It would help reinforce the concept.
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