Question:
Beena got married 8 years ago. Today, her age is \(\frac {11}{4}\) times her age at the time of marriage. If her daughter‘s age is \(\frac {1}{10}\) times her age, then her daughter‘s age is:
Beena got married 8 years ago. Today, her age is \(\frac {11}{4}\) times her age at the time of marriage. If her daughter‘s age is \(\frac {1}{10}\) times her age, then her daughter‘s age is:
Updated On: Jul 15, 2026
- 3 years
- 4 years
- 5 years
- 2 years
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The Correct Option is B
Approach Solution - 1
The correct option is (B): 4 years .
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The question says Beena got married 8 years ago, her present age is 1 1/4 times her age at marriage, and her daughter's age is 1/10th of her present age, asking for the daughter's age. Since her present age must satisfy both the "8 years since marriage" fact and the "1 1/4 times" ratio at once, we can test each option by working backward from the daughter's age to check consistency.
- 3 years: A daughter's age of 3 implies Beena's present age is \( 3 \times 10 = 30 \). Her age at marriage would then be \( 30-8=22 \). Checking the ratio, \( 30 \div 22 \) is not 1 1/4, so this does not fit.
- 4 years: A daughter's age of 4 implies Beena's present age is \( 4 \times 10 = 40 \). Her age at marriage would then be \( 40-8=32 \). Checking the ratio, \( 40 \div 32 = 1.25 \), which is exactly 1 1/4. This satisfies both conditions at once.
- 5 years: A daughter's age of 5 implies Beena's present age is \( 5 \times 10 = 50 \). Her age at marriage would then be \( 50-8=42 \). Checking the ratio, \( 50 \div 42 \) is not 1 1/4, so this fails.
- 2 years: A daughter's age of 2 implies Beena's present age is \( 2 \times 10 = 20 \). Her age at marriage would then be \( 20-8=12 \), which is not a realistic marriage age and also does not give a 1 1/4 ratio when checked.
Only a present age of 40, giving a marriage age of 32, satisfies the 1 1/4 times relationship described in the question, which fixes the daughter's age.
Therefore, the correct answer is 4 years.
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Approach Solution -3
The question says Beena got married 8 years ago, her present age is one and a quarter times her age at marriage, and her daughter is one tenth of her present age, then asks for the daughter's age. Setting up her age at marriage as a single unknown and solving the resulting equation directly gives her present age, which then fixes the daughter's age.
- 3 years: If the daughter is 3, Beena's present age would be \( 3\times10=30 \), which through the equation below does not correspond to a marriage age satisfying the given one-and-a-quarter relationship.
- 4 years: Let Beena's age at marriage be \( m \). Her present age is \( m+8 \), and this equals \( \frac{5}{4}m \). Solving, \( 4(m+8)=5m \), so \( 4m+32=5m \), giving \( m=32 \). Her present age is then \( 32+8=40 \), and the daughter's age is \( \frac{1}{10}\times40=4 \), matching this option.
- 5 years: A daughter's age of 5 would need Beena's present age to be 50, which the equation above does not produce from any consistent marriage age.
- 2 years: A daughter's age of 2 would need Beena's present age to be 20, again not a value the equation supports, and it would also imply an implausibly young marriage age.
Solving the marriage-age equation directly gives \( m=32 \) and a present age of 40, which fixes the daughter's age at exactly 4 years.
Therefore, the correct answer is 4 years.
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