10. Lakshmi is 24 vears older than her daughter Priya. 6 years ago
was thrice that of Priya. If Priya's present age is x then,
i) Find the present age of Lakshmi in terms of x.
ii) Find the ages of Priya and Lakshmi 6 years ago in terms of x.
iii) Find the present ages of Priya and Lakshmi (in years)?
(OR)
Answers
If Priya's present age is x then, the present age of Lakshmi in terms of x is (x + 24), the ages of Priya and Lakshmi 6 years ago are (x-6) & (x+18) respectively and the present ages of Priya and Lakshmi (in years) are 18 & 42 years respectively.
Step-by-step explanation:
Case (i): Present Age of Lakshmi in terms of x
It is given that Priya’s present age is x years
Lakshmi is 24 years older than Priya currently
∴ The present age of Lakshmi will be = (x + 24) years
Case (ii): Ages of Priya and Lakshmi 6 years ago in terms of x
6 years ago:
Priya’s age was = (x – 6) years
and,
Lakshmi’s age was = (x+24-6) = (x+18) years
Case (iii): Present ages of Priya and Lakshmi (in years)
It is given that 6 years ago Lakshmi was thrice the age of Priya, so we can write the equation as,
x + 18 = 3(x - 6)
⇒ x + 18 = 3x – 18
⇒ 2x = 36
⇒ x = 18 years ← Present age of Priya in years
and,
Present age of Lakshmi in terms of years = x + 24 = 18 + 24 = 42 years
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