The age of Sonal and Nitya are in the ratio of 9 : 5 respectively. After 8 years the ratio of their ages will be 13 : 9. What is the difference in years between their ages?
The age of Sonal and Nitya are in the ratio of 9 : 5 respectively. After 8 years the ratio of their ages will be 13 : 9. What is the difference in years between their ages?
A4 years
B12 years
C6 years
DNone of these
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Correct answer is: None of these
Explanation:
The age of Sonal and Nitya are in the ratio of 9:5 respectively
Let x be an arbitrary constant,
Age of Sonal is 9x and age of Nitya is 5x.
After 8 years the ratio of their age is 13 : 9
Now,
After 8 years Sonal’s age will be (9x + 8)
After 8 years Nitya’s age will be (5x + 8)
According to the question
\(\frac{{\left( {9x\; + \;8} \right)}}{{\left( {5x\; + \;8} \right)}}\; = \;\frac{{13}}{9}\)
\(⇒ 81x + 72 = 65x + 104\)
\(⇒ 16x = 32\)
\(⇒ x = 2\)
Sonal’s age is 9 × 2 = 18 years
Nitya’s age is 5 × 2 = 10 years
And their age difference is (18 - 10) years = 8 years
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