Question

a mother is 7 times as old as her daughter. two years ago, the mother was 13times as old as her daughter. Find their present age...please give stepwise answer​

Answer 1

Given:-

• Present age of mother = 7(Present age of her daughter)
• Two years ago, age of mother = 13(Age of her daughter)

To find:-

• Present age of daughter.
• Present age of mother.

Answer:-

Present age:

▪Let the present age of daughter be x years

▪Then the present age of the mother is 7x years

Two years ago:

▪Age of daughter = (Present age of daughter) - 2

= (x - 2) years

▪Age of mother = (Present age of mother) - 2

= (7x - 2) years

According to the question,

Two years ago, age of mother = 13(age of her daughter)

So,

7x - 2 = 13(x - 2)

→ 7x - 2 = 13x - 26

→ 13x - 7x = 26 - 2

→ 6x = 24

→ x = 4

Hence,

• Present age of daughter = x years = 4 years
• Present age of mother = 7x years = (7 * 4) years = 28 years

Answer 2

Answer:

Given :-

• A mother is 7 times as old as her daughter age. After two years ago the mother was 13 times old as her daughter.

To Find :-

• What is their present ages.

Solution :-

Let, the present age of daughter be x years

And, the present age of mother be 7x years

After 2 years,

Age of daughter will be x - 2 years

And, the age of mother will be 7x - 2 years

According to the question,

⇒ 13(x - 2) = 7x - 2

⇒ 13x - 26 = 7x - 2

⇒ 13x - 7x = - 2 + 26

⇒ 6x = 24

⇒ x = 24/6

➠ x = 4

Hence, the required ages are,

✧ Present age of daughter = x = 4 years

✧ Present age of mother = 7x = 7(4) = 28 years

∴ The present age of daughter is 4 years and the present age of mother is 28 years .

Let's Verify :-

↦ 13(x - 2) = 7x - 2

↦ 13x - 26 = 7x - 2

Put x = 4 we get,

↦ 13(4) - 26 = 7(4) - 2

↦ 52 - 26 = 28 - 2

↦ 26 = 26

➦ LHS = RHS

Hence, Verified ✔