Question

40 The mother's age is six times her daughter's age. Four years hence, the age of the mother will be four times her daughter's age. The ratio of present ages, of the daughter and the mother are, respectively

(a) 5:2 (b) 2:5 (0)1:6 (4) 6:1​

Answer 1

Answer:

LET THE DAUGHTER AGE BE X

MOTHERS AGE =6x

AGE OF DAUGHTER AND MOTHER FOUR YEARS HENCE WLL BE

DAUGHTER'S AGE =  x+4

MOTHERS AGE = 4(x+4) =4x+16

6x+4=4x+16

6x-4x=16-4

2x=12

x=12/2

daughter's present age=6yr

mothers present age=6*6=36

ratio : 6/36= 1:6

Explanation:

Answer 2

Correct Question

The mother's age is six times her daughter's age. Four years from now, the age of the mother will be four times her daughter's age. The ratio of present ages, of the daughter and the mother are,

(a) 5:2 (b) 2:5 (c)1:6 (d) 6:1​

Answer:

The ratio of present ages, of the daughter and the mother are 1:6 and option (c) is correct.

Explanation:

Given:

The mother's age is six times her daughter's age.

Four years hence, the age of the mother will be four times her daughter's age.

To Find:

The ratio of present ages, of the daughter and the mother.

Solution:

Let the  present ages, of the daughter and the mother are p and q respectively.

As given,the mother's age is six times her daughter's age.

$q=6p$  ---------  equation no.01.

As given,four years from now, the age of the mother will be four times her daughter's age.

$q+4= 4(p+4)$

$q+4= 4p+16$

$q= 4p+12$  ------- equation no.02.

Putting the value of q from equation no.01 to equation no.02, we get.

$6p= 4p+12$

$2p=12$

$p=6\ years$

Putting the value of p in equation no.01, we get.

$q=6\times 6$

$q=36\ years$

The ratio of present ages, of the daughter and the mother $=\frac{p}{q} =\frac{6}{36}$

                                                                                                          $=\frac{1}{6}$

                                                                                                          $=1:6$

Thus,the ratio of present ages, of the daughter and the mother 1:6 and option (c) is correct.

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