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The ages of A and B are in the ratio 4:5. After 5 years, the ratio becomes 5:6. What is the current age of A?
20
25
30
35
20
Notice the difference between the ratio terms: 4 to 5 is 1 part, and 5 to 6 is 1 part. Since 1 unit increase corresponds to 5 years, 4 units for A equals 4 ├Ч5=20years.
Ratio of current ages of A and B = 4:5, Ratio of ages after 5 years = 5:6, Time period = 5 years
5x+54x+5тАЛ=65тАЛ
Notice the difference between the ratio terms: 4 to 5 is 1 part, and 5 to 6 is 1 part. Since 1 unit increase corresponds to 5 years, 4 units for A equals 4 ├Ч5=20years.
Students often make mistakes by adding 5 directly to the ratio terms instead of working with variables like 4x and 5x.
Assume Current Ages
Let the current ages of A and B be 4x and 5x based on the given ratio of 4:5.
AgeAтАЛ=4x,AgeBтАЛ=5x
Set Up Equation for Future Ages
After 5 years, the age of A becomes 4x+5 and the age of B becomes 5x+5. The new ratio is given as 5:6.
5x+54x+5тАЛ=65тАЛ
Solve the Linear Equation
Cross-multiply the equation to solve for x: 6(4x+5)=5(5x+5) which simplifies to 24x+30=25x+25.
x=5
Calculate Current Age of A
Substitute the value of x back into A's current age expression 4x.
4├Ч5=20
A is correct because solving the age ratio equation yields x=5, resulting in A's current age being 4├Ч5=20 years.
Age problems are a direct application of ratio and proportion principles that also extend to mixture and partnership problems in quantitative aptitude.
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