Question

Three years ago, the ratio of ages of A and B was 7:1. After three years from now, the ratio of their ages will
be 4:1. What is the difference between their ages (in years) after seven years from now?
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Answer 1

$\huge {\pink {\sf{\underline {\underline {Question:-}}}}}$

Three years ago, the ratio of ages of A and B was 7:1. After three years from now, the ratio of their ages will be 4:1. What is the difference between their ages (in years) after seven years from now?

$\huge {\green {\sf{\underline {\underline {Answer:-}}}}}$

Let the present ages of A amd B be " x " and " y " respectively.

Then ,

3 years ago

Age of A = x - 3 and Age of B = y - 3

3 years hence

Age of A = x + 3 and Age of B = y + 3

Acc to given data ,

$\huge {\sf { \frac {x-3}{y-3} = \frac {7}{1}} }$

${ \sf{ x - 3 = (y - 3 ) 7 } }$

${\sf {x - 3 = 7y - 21 }}$

${ \sf {\blue {\boxed { 7y - x = 18 ....... ( 1 ) } }}}$

and ,

$\huge {\sf { \frac {x+3}{y+3} = \frac {4}{1}} }$

${ \sf{ x + 3 = (y + 3 ) 4} }$

${\sf {x + 3 = 4y + 12 }}$

${ \sf {\blue {\boxed { 4y - x = - 9 ........ ( 2 ) }}}}$

Subract equation ( 2 ) from equation ( 1 )

${\sf{( 7y - x ) - (4y - x ) = 18 - ( - 9 )}}$

${\sf{3y = 27 \implies y = 9 }}$

Substitute the value of y in equation ( 1 )

${ \sf { 7(9) - x = 18 \implies 63 - x = 18 \implies x = 63 - 18 = 45 }}$

After 7 years

Age of A = x + 7 = 45 + 7 = 52

Age of B = y + 7 = 9 + 7 = 16

Difference between their ages = 52 - 16 = 36

${\sf {\orange{\underline { The\: difference\: between\: their\: ages\: after\: seven\: years \:from \: now\: is \: 36\: years }}}}$