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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 sum of the present age of Amit and Amita?
70 years
40 years
50 years
60 years
60 years
Since the ratio 5 years ago and 5 years hence is 1:1, it implies (AmitтИТ5)=(Amita+5), therefore AmitтИТAmita=10. The ratio difference 7xтИТ5x=2x corresponds to 10, so 2x=10тЗТx=5.
Ratio of present ages of Amit and Amita is 7:5. Ratio of Amit's age 5 years ago to Amita's age 5 years hence is 1:1.
5x+57xтИТ5тАЛ=1
Since the ratio 5 years ago and 5 years hence is 1:1, it implies (AmitтИТ5)=(Amita+5), therefore AmitтИТAmita=10. The ratio difference 7xтИТ5x=2x corresponds to 10, so 2x=10тЗТx=5.
Students often confuse '5 years ago' and '5 years hence' or perform 7xтИТ5=5xтИТ5, leading to incorrect results by ignoring the time displacement.
Define ages based on ratio
Let the present ages of Amit and Amita be 7x and 5x respectively.
Amit=7x,Amita=5x
Apply given age conditions
Amit's age 5 years ago is 7xтИТ5. Amita's age 5 years hence is 5x+5. The ratio is given as 1:1.
5x+57xтИТ5тАЛ=11тАЛ
Solve for x
Cross-multiplying gives 7xтИТ5=5x+5, which simplifies to 2x=10, so x=5.
x=5
Calculate the sum of present ages
The sum of their present ages is 7x+5x=12x. Substituting x=5, we get 12├Ч5=60.
12├Ч5=60┬аyears
D is correct because the sum of their present ages is 60 years.
Age problems can always be solved by equating the difference in ages, as the difference between two individuals' ages remains constant over time.
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