Question

wer.
1. The ratio of the present ages of a mother and her
daughter is 7 : 1. Four years ago, the ratio of their
ages was 19:1. What will be the mother's
age
four
(S.B.L. P.O., 2010)
years from now?​

Answer 1

Required Answer:-

We have:

• The ratio of the present ages of a mother and her
• daughter is 7 : 1
• Four years ago, the ratio of their ages was 19 : 1.

To FinD:

• What will be the mother's age four years from now?

Step-by-Step Explanation:

Let the ages of mother and daughter be x and y respectively.

According to condition -(1)

➛ x : y = 7 : 1

By the principle of proportion, Product of means = Product of extremes.

➛ x = 7y --------(1)

According to condition -(2)

➛ x - 4 : y - 4 = 19 : 1

Again by the principle of proportion, Product of means = Product of extremes.

➛ x - 4 = 19(y - 4)

➛ x - 4 = 19y - 76

➛ x - 19y = -72 ------(2)

Substituting x = 7y in equation (2),

➛ 7y - 19y = -72

➛ -12y = -72

➛ y = 6

Then, x = 42

Therefore:-

• The age of the mother after 4 years will be 42 + 4 = $\boxed{\bf{46 \:years}}$

Answer 2

Answer:

Step-by-step explanation:

Given, the ratio of their present ages is 7 : 1

let the age of her daughter be $x$ so age of mother will be $7x$

their ages before four years will be

mother - $7x-4$

daughter - $x-4$

According  to the question,

        $\frac{7x-4}{x-4}$ = $\frac{19}{1}$

      $7x-4$ = $19x$$-76$

      $12x$ = $72$

      $x = 6$

age of daughter is 6 years and age of her mother is 6 * 7 = 42 years

hence, the present age of mother is 42 years and the age of daughter is 6 years.

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