Question

Today the ratio of elinor's age is 3:8 to his mother after 15 years ,the ratio will become 6:11. Find elinor's age today and find her mothers age after 15 years.

Answer 1

Given

ratio of elinor's age to his mother is 3 : 8

after 15 years

 the ratio will become 6:11

Find out the  elinor's age today and find her mothers age after 15 years.

To proof

As given in the question

ratio of elinor's age to his mother is 3 : 8

let x be the variable describe age.

let the elinor age = 3x

let the mother age = 8x

after 15 years

ratio will become 6:11

$\frac{elinor\ age + 15 }{Mother\ age + 15 } = \frac{6}{11}$

As assume ealier elinor age be 3x and mother age be 8x

put this in the above equation

we get

$\frac{3x + 15 }{8x + 15 } = \frac{6}{11}$

now sloving the above equation

we get

11 ( 3x + 15) = 6 ( 8x + 15 )

33x + 165 = 48x + 90

75 = 15x

$x = \frac{75}{15}$

x = 5

Therefore

elinor's age today = 3x

                              = 3 × 5

                              = 15years

mothers age after 15 years = 8x + 15

                                              = 8× 5 + 15

                                              = 40 + 15

                                              = 55years

Hence proved