Question

A) Lakshmi is 24 years older than her daughter Priya. 6 years ago Lakshmi's
age 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​

Answer 1

Answer:

Lakshmi 18 Priya 24 years and the both will be same

Answer 2

i) Present age of Lakshmi is $x+24$ years.

ii) Present age of Priya and Lakshmi 6 years ago are $x-6$ years and either $x+18\ or\ 3x-18$ years respectively.

iii) Present age of Priya is 18 years and present age of Lakshmi is 42 years.

Step-by-step explanation:

(i)

Given:

Present age of Priya is 'x'.

Lakshmi is 24 years than Priya. Therefore, we need to add 24 to present age of Priya. So,

Lakshmi's present is equal to $x+24$ years.

(ii)

6 years ago means we need to subtract 6 from their present ages.

Therefore, the age of Priya 6 years ago is equal to $x-6$ years.

Lakshmi's age 6 years ago = Present age - 6 = $x+24-6=x+18$

Also, as per question, 6 years ago, Lakshmi's age is thrice of Priya which is equal to $3(x-6)=3x-18$

Therefore, Lakshmi's age 6 years ago is either $x+18\ or\ 3x-18$ years.

(iii)

As per question, Lakshmi's age 6 years ago is thrice that of Priya's age 6 years ago. Therefore,

$x+18=3(x-6)\\x+18=3x-18\\3x-x=18+18\\2x=36\\x=\frac{36}{2}=18$

Therefore, present age of Priya is 18 years.

Present age of Lakshmi is 24 more than that of Priya. So, 24 + 18 = 42 years.