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# The Ratio of Present Ages of Rehana and Her Mother is 2 : 7. After 2 Years, the Ratio of Their Ages Will Be 1 : 3. What is Rehana'S Present Age ? - Algebra

Sum

The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3. What is Rehana's present age ?

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#### Solution

Let the present ages of Rehana and her mother be 2x years and 7x years, respectively.
After 2 years,
Age of Rehana = (2x + 2) years
Age of Rehana's mother = (7x + 2) years
It is given that after 2 years, the ratio of their ages will be 1 : 3.
∴ ( 2x + 2)/( 7x + 2) = 1/3
⇒ 6x + 6 = 7x + 2
⇒ 7x - 6x = 6 - 2
⇒ x = 4
∴ Rehana's present age = 2x = 2 × 4 = 8 years
Thus, the present age of Rehana is 8 years.

Concept: Properties of Ratio
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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Practice Set 4.1 | Q 8 | Page 61
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