Ankita is $18 y e a r s$ old and her brother Apoorv is $16 y e a r s$ old. What is the ratio of Ankita's age to Apoorv's age? What will be the ratio of Apoorv's age to Ankita's age after $8$ years?

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Solution

Age of Ankita is $18 y e a r s$ old.
Age of her brother Apoorv is $16 y e a r s$ old
Step 1: We can write $18 : 16$ as $\frac{18}{16}$
Step 2: Find the HCF of numerator 18 and denominator 16.
By the method of prime factorisation,
$18 = 2 \times 3^{2}$
$16 = 2^{4}$
$H C F (18, 16) = 2$
Step 3: Divide both the numerator and denominator by HCF
$\Rightarrow$ $\frac{18 \div 2}{16 \div 2}$
$\Rightarrow$ $\frac{9}{8}$
Therefore, $18 : 16$ can be expressed in simplest form as $9 : 8$
Ratio of Ankita's age to Apoorv's age is $9 : 8$
Step 5: After $8$ years,
Ankita age becomes $18 + 8 y e a r s = 26 y e a r s$
Her brother Apoorv age becomes $16 + 8 y e a r s = 24 y e a r s$
Step 6: We can write $24 : 26$ as $\frac{24}{26}$
Step 7: Find the HCF of numerator $24$ and denominator $26$ .
By the method of prime factorisation,
$24 = 2^{3} \times 3$
$26 = 2 \times 13$
$H C F (24, 26) = 2$
Step 8: Divide both the numerator and denominator by HCF
$\Rightarrow$ $\frac{24 \div 2}{26 \div 2}$
$\Rightarrow$ $\frac{12}{13}$
Therefore, $24 : 26$ can be expressed in simplest form as $12 : 13$
Ratio of Apoorv's age to Ankita's age after $8$ years is $12 : 13$

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Ankita is 18years old and her brother Apoorv is 16years old. What is the ratio of Ankita's age to Apoorv's age? What will be the ratio of Apoorv's age to Ankita's age after 8 years?

Ankita is $18 y e a r s$ old and her brother Apoorv is $16 y e a r s$ old. What is the ratio of Ankita's age to Apoorv's age? What will be the ratio of Apoorv's age to Ankita's age after $8$ years?