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The ratio between the present ages of Amit and Amita is 7:5, respectively. The ratio between Amit's age 5 years ago and Amita's age 5 years hence is 1:1. What is the ratio between Amit's age 5 years hence and Amita's age 5 years ago?
2
1
3
2
2
Express ages in terms of a common variable x. Since AтИТ5=B+5, substitute 7xтИТ5=5x+5 to find x=5. Then calculate required ages: Amit in 5 years = 7(5)+5=40 and Amita 5 years ago = 5(5)тИТ5=20. The ratio is 40:20=2:1.
Ratio of present ages of Amit (A) and Amita (B) = 7:5. Ratio of (Amit - 5) years to (Amita + 5) years = 1:1.
A=7x,B=5x
Express ages in terms of a common variable x. Since AтИТ5=B+5, substitute 7xтИТ5=5x+5 to find x=5. Then calculate required ages: Amit in 5 years = 7(5)+5=40 and Amita 5 years ago = 5(5)тИТ5=20. The ratio is 40:20=2:1.
Students often swap the directions of the time shift (subtracting vs adding years) or calculate the ratio in the wrong order.
Define ages in terms of x
Let the present age of Amit be 7x and Amita be 5x.
A=7x,B=5x
Set up the equation
Given the ratio of Amit's age 5 years ago to Amita's age 5 years hence is 1:1, we write: 5x+57xтИТ5тАЛ=11тАЛ.
7xтИТ5=5x+5
Solve for x
Rearranging terms gives 7xтИТ5x=5+5, which simplifies to 2x=10, so x=5.
x=5
Calculate required ages
Amit's age 5 years hence is 7(5)+5=40. Amita's age 5 years ago is 5(5)тИТ5=20.
Ratio=2040тАЛ=12тАЛ
B is correct because the ratio between Amit's age 5 years hence (40) and Amita's age 5 years ago (20) simplifies to 2:1.
This type of ratio problem is frequently asked in various competitive exams; always represent ages using a common variable to quickly solve for the unknown.
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