Seema is twice as old as Alka. If nine years is subtracted from Alka's age and six years is added to Seema's age, then Seema will be four times Alka's age. How old was Alka three years ago?
18 years
Let Alka's current age be \( x \) years. Since Seema is twice as old as Alka, Seema's current age would be \( 2x \) years.
According to the problem, if nine years are subtracted from Alka's age, her age becomes \( x - 9 \) years. Also, if six years are added to Seema's age, her age becomes \( 2x + 6 \) years. The problem states that under these conditions, Seema's age is four times Alka's age:
\( 2x + 6 = 4(x - 9) \).
Now, solve the equation:
- Expand the equation: \( 2x + 6 = 4x - 36 \).
- Rearrange terms to one side: \( 6 + 36 = 4x - 2x \).
- Simplify: \( 42 = 2x \).
- Divide by 2 to find \( x \): \( x = 21 \).
Alka's current age is 21 years. Therefore, Alka's age three years ago was \( 21 - 3 = 18 \) years old. Hence, the correct answer is:
18 years
Similar Questions
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Important Questions from Problems on Age
The age of Dr. Pandey is four times the age of his son. After 10 years, the age of Dr. Pandey will be twice the age of his son. The present age of Dr. Pandey's son is?
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- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
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