Question

neha mother's is 20 years older than her. she was three times as old as neha ten years ago. find their present age.​

Answer 1

Given:-

• At present Neha's mother is 29yrs older than her.
• 10yrs ago her mother was 3time her daughter's age.

Find:-

• Their Present Ages.

Solution:-

Let, Present Age of Neha be 'x' yrs

and Present Age of her mother be 'y' yrs

Now,

$\qquad\ast\underline{\text{According To Question:}}$

At, present Neha's mother is 20yrs older than her.

$\sf \implies y = x + 20 \qquad\bigg\lgroup Equation\:1 \bigg\rgroup$

10yrs ago mother was thrice the age of her daughter.

$\sf \implies y - 10 = 3(x - 10) \qquad\bigg\lgroup Equation\:2 \bigg\rgroup$

$\bigstar\underline{\text{Using Eq.1 in Eq.2}}$

$\sf \dashrightarrow y - 10 = 3(x - 10)$

$\sf \dashrightarrow (x + 20)- 10 = 3(x - 10)$

$\sf \dashrightarrow x + 20- 10 = 3(x - 10)$

$\sf \dashrightarrow x + 10 = 3x - 30$

$\sf \dashrightarrow x - 3x =- 30 - 10$

$\sf \dashrightarrow- 2x =- 40$

$\sf \dashrightarrow \not- 2x = \not- 40$

$\sf \dashrightarrow 2x =40$

$\sf \dashrightarrow x = \dfrac{40}{2}$

$\sf \dashrightarrow x =20yrs$

$\bigstar\underline{\text{Using value of x in Eq.1}}$

$\sf \dashrightarrow y = x + 20$

$\sf \dashrightarrow y =20+ 20$

$\sf \dashrightarrow y =40yrs$

___________________________

$\underline{\boxed{ \sf\therefore Age \: of \: Neha, x = 20yrs}}$

$\underline{\boxed{ \sf\therefore Age \: of \: Neha's \: mother, y = 40yrs}}$