Question

the ratio of mothers age to that of her daughters age is 7: 2 if the sum of their ages is 54 , then the age of mothers is
a. 40
b. 48
c. 42
d. 45​

Answer 1

Given :

• Ratio of mother and daughters age = 7 : 2
• Sum of their age = 54

To find :

• Age of mother

According to the question,

➞ Let the ratio be 7x and 2x

➞ 7x + 2x = 54

➞ 9x = 54

➞ x = 54 ÷ 9

➞ x = 6

Value of 7x :

➞ 7x

➞ 7(6)

➞ 42

Value of 2x :

➞ 2x

➞ 2(6)

➞ 12

• So, the age of mother is 42 years.

∴ Option c) 42 is correct.

_____________________

Verification :

➞ 7x + 2x = 54

➞ Putting the value of x is 6

➞ 7(6) + 2(6) = 54

➞ 42 + 12 = 54

➞ 54 = 54

∴ L.H.S = R.H.S

Hence, Verified.

Answer 2

Answer:

Given :-

• The ratio of mother age to that of her daughter's age is 7:2. The sum of their ages is 54.

To Find :-

• What is the age of mother.

Solution :-

Let, the age of mother age be 7x

And, the age of her daughter's be 2x

Their sum of their ages is 54

According to the question,

⇒ 7x + 2x = 54

⇒ 9x = 54

⇒ x = 54 ÷ 9

➠ x = 6

Hence, their ages will be,

✧ Age of mother = 7x = 7 × 6 = 42 years

✧ Age of her daughter = 2 × 6 = 12 years

∴ The age of mother is 42 years .

Correct options is option no (c) 42 years.

Let's Verify :-

↦ 7x + 2x = 54

Put x = 6

↦ 7 × 6 + 2 × 6 = 54

↦ 42 + 12 = 54

↦ 54 = 54

➦ LHS = RHS

Hence, Verified ✔