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Anu is two years older than Kanu, who is twice as old as Tanu. If the total of their ages is 32, then what is the age of Kanu?
8 years
7 years
12 years
14 years
12 years
Represent all ages in terms of Tanu (x). Kanu is 2x, Anu is 2x+2. Sum is x+2x+2x+2=32, so 5x=30, x=6. Kanu is 2x=12.
Anu is 2 years older than Kanu. Kanu is twice as old as Tanu. The sum of their ages is 32 years.
T+2T+(2T+2)=32
Represent all ages in terms of Tanu (x). Kanu is 2x, Anu is 2x+2. Sum is x+2x+2x+2=32, so 5x=30, x=6. Kanu is 2x=12.
Students often assign the variables incorrectly (e.g., assigning Anu as the base variable instead of the youngest person, Tanu), leading to wrong algebraic setup.
Define variables
Let Tanu's age be x. Since Kanu is twice as old as Tanu, Kanu's age = 2x. Anu is 2 years older than Kanu, so Anu's age = 2x+2.
Tanu=x,Kanu=2x,Anu=2x+2
Form the equation
The sum of their ages is given as 32. Combine the expressions for their ages.
x+2x+(2x+2)=32
Solve for x
Simplify the equation: 5x+2=32, which simplifies to 5x=30, resulting in x=6.
5x=30тЗТx=6
Calculate Kanu's age
Kanu's age is 2x. Substitute x=6 into this expression.
Kanu=2├Ч6=12
C is correct because the calculation yields 12 years.
This type of age-based ratio problem is common in competitive exams; always define the youngest person as 'x' to simplify the linear equation setup.
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