Question

2 years ago your mother was four times as old as her daughter 8 year hence mother's age will exceed her daughter age by 12 years the ratio of present age of mother and daughter is​

Answer 1

Step-by-step explanation:

Let,

  Daughter's age, 2 years ago, was a years

  Mother's age, 2 years ago, was 4a years [ 4 times of a years or daughter's age ]

Therefore,

Present age of daughter = ( a + 2 ) years

Present age of mother = ( 4a + 2 ) years

After 8 years, ages will be increased  by 8 years :

Age of daughter after 8 years = ( a + 2 + 8 ) years = ( a + 10 ) years

Age of mother after 8 years = ( 4a + 2 + 8 ) years = ( 4a + 10 ) years

According to the question : -

= > Mother's age will exceed daughter's age by 12 years

= > ( 4a + 10 ) years = ( a + 10 ) years + 12 years

= > 4a + 10 = a + 10 + 12

= > 4a + 10 = a + 10 + 12

= > 4a - a + 10 - 10 = 12

= > 3a = 1 2

= > a = 12 / 3

= > a = 4

Hence,

Ratio of present of mother and daughter = ( present age of mother or 4a + 2 years ) : ( present age of daughter or a + 2 years )

= > Required ratio = { 4( 4 ) + 2 } : { 4 + 2 }

= > Required rattio = { 16 + 2 } : { 6 }

= > Required ratio = 18 : 6

= > Required ratio = 3 : 1

Therefore the ratio of present ages of mother and daughter is 3 : 1.

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