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The ratio of ages of A and B is 3:4. After 5 years, the ratio becomes 4:5. What is the current age of A?
15 years
20 years
12 years
18 years
15 years
Since the unit increment for both A and B is uniform (4-3=1 unit, 5-4=1 unit) corresponding to 5 years, 1 unit = 5 years. A's current age = 3 units = 3 * 5 = 15 years.
Initial ratio of ages of A and B is 3:4, ratio after 5 years is 4:5
4x+53x+5тАЛ=54тАЛ
Since the unit increment for both A and B is uniform (4-3=1 unit, 5-4=1 unit) corresponding to 5 years, 1 unit = 5 years. A's current age = 3 units = 3 * 5 = 15 years.
Forgetting that age differences between two individuals remain constant or miscalculating the cross-multiplication expansion.
Assume current ages
Let current ages of A and B be 3x and 4x based on the given ratio 3:4.
A=3x,B=4x
Form equation after 5 years
Add 5 years to both ages and set equal to the new ratio 54тАЛ.
4x+53x+5тАЛ=54тАЛ
Solve for x
Cross-multiply: 5(3x+5)=4(4x+5)тЯ╣15x+25=16x+20тЯ╣x=5.
x=5
Calculate A's current age
Substitute x=5 into A's current age 3x.
3├Ч5=15┬аyears
A is correct because the current age of A is 15 years.
Check for uniform unit increments across ratio shifts first; it bypasses quadratic/simultaneous equation setups in 10 seconds.
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