Question

The ratio of ages of Abha and her mother is 2:5. At the time of Abha's birth her mothers
age was 27 year. Find the present ages of Abha and her mother.
Answer:
1Abha's age18, mother's age45
2Abha's age19, mother's age43
3Abha's age15, mother's age41​

Answer 1

✪ Given :

• Ratio of ages of Abha and her mother is 2:5.
• At the time of Abha's birth her mother's age was 27 years.

------------------------------------------------------

✪ To Find :

• Their present ages.

------------------------------------------------------

✪ Calculation :

Supposition :- Let us suppose the present ages of Abha and her mother as

➽ 2x (Abha's age)

➽ 5x (Abha's mother's age)

According to the question :

⇒ 5x - 2x = 27

⇒ 3x = 27

⇒ x = 27/3

⇒ x = 9 years

Now, present ages of Abha and her mother is -

≛ Present age of Abha :

→ 9 × 2

→ 18 years

≛ Present age of her mother :

→ 9 × 5

→ 45 years

Therefore

• Present age of Abha is 18 years
• Present age of Abha's mother is 45 years

Answer 2

AnswEr :

❍ Given that, the ratio of ages of Abha and Her mother is 2: 5. So, let's say that the present ages of Abha and her mother be 2x and 5x respectively.

⭒ By given C O N D I T I O N :

• At the time of Abha's Birthday, her mother was 27 years old.

⠀⠀⠀

Therefore,

⠀⠀⠀

$\dashrightarrow\sf 5x - 2x = 27 \\\\\\\dashrightarrow\sf 3x = 27 \\\\\\\dashrightarrow\sf x = \cancel\dfrac{27}{3}\\\\\\\dashrightarrow\underline{\boxed{\frak{\pmb{\purple{x = 9}}}}}\;\bigstar$

⠀⠀⠀

Hence,

⠀⠀☆ Abha's present age is 2x = 2(9) = 18 years.

⠀⠀☆ Abha's mother's present age is 5x = 5(9) = 45 ⠀⠀⠀⠀years.

⠀⠀⠀

$\therefore{\underline{\textsf{Hence,\; \textbf{Option A)}\;present\;age\;of\;Abha\;\&\;her\; mother\;is\; \textbf{18 years}\:\sf{and}\;\textbf{45 years}.}}}$

⠀⠀⠀