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Ishan is younger than Surya by 3 years. If the ages of Ishan and Surya are in the ratio 7:8, then how old is Ishan?
27 years
21 years
18 years
24 years
21 years
Since the ratio difference is 8тИТ7=1 part and the actual age difference is 3 years, 1 part equals 3 years. Therefore, Ishan's age is 7├Ч3=21 years.
Age ratio of Ishan to Surya = 7 : 8, Difference in age = 3 years.
AgeIтАЛ=7x,AgeSтАЛ=8x,AgeSтАЛтИТAgeIтАЛ=3
Since the ratio difference is 8тИТ7=1 part and the actual age difference is 3 years, 1 part equals 3 years. Therefore, Ishan's age is 7├Ч3=21 years.
Students often swap the ratio parts, calculating Surya's age (24) instead of Ishan's (21), or misinterpreting 'younger' as an addition instead of a difference.
Define ages using ratio
Let the common multiplier for the ratio be x. Given the ratio of Ishan to Surya is 7:8, we represent their ages as 7x and 8x respectively.
AgeIтАЛ=7x,AgeSтАЛ=8x
Set up the difference equation
The problem states that Ishan is 3 years younger than Surya. This means the difference between their ages is 3 years.
8xтИТ7x=3
Solve for x
Simplifying the equation gives the value of the common multiplier x.
x=3
Calculate Ishan's age
Substitute x=3 back into the expression for Ishan's age (7x).
AgeIтАЛ=7├Ч3=21
B is correct because Ishan's age is calculated as 7├Ч3=21 years.
Age problems are common in quantitative aptitude; always use the 'unit' method (parts) to solve ratio differences quickly without framing complex algebraic variables.
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