Question

Three years ago , the ratio of ages of ravi and siva was 14 : 1 .After three years from now , the ratio of their ages will be 8 : 1 . What is the differnce between their ages after 10 years from now .

Answer 1

Step-by-step explanation:

The ratio of Hari's and Harry's present ages is 5:7

So, let their ages be 5x and 7x

After 4 years their ages will be in ratio 3:4

Therefore,(5x+4)/(7x+4)=3/4

or, 4(5x+4)=3(7x+4)

or, 20x+16=21x+12

or, 16−12=21x−20x

or, 4=1x

or, x=4

Therefore, present age of Hari = 5x=(5×4)=20 years.

Present age of Harry =7x=(7×4)=28 years

The sum of their age is 28+20=48years

Answer 2

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

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 ,

$\huge {\sf { \frac {x-3}{y-3} = \frac {14}{1}} }$

${ \sf{ x - 3 = (y - 3 ) 14 } }$

${\sf {x - 3 = 14y - 42 }}$

${ \sf {\blue {\boxed { 14y - x = 39 ....... ( 1 ) } }}}$

and ,

$\huge {\sf { \frac {x+3}{y+3} = \frac {8}{1}} }$

${ \sf{ x + 3 = (y + 3 ) 8} }$

${\sf {x + 3 = 8y + 24 }}$

${ \sf {\blue {\boxed { 8y - x = -21 ....... ( 2 ) }}}}$

Subract equation ( 2 ) from equation ( 1 )

${\sf{( 14y - x ) - (8y - x ) = 39 - ( - 21 )}}$

${\sf{6y = 60 \implies y = 10 }}$

Substitute the value of y in equation ( 1 )

${ \sf { 14(10) - x = 39 \implies 140 - x = 39 \implies x = 140 - 39 = 101 }}$

After 10 years

Age of A = x + 10 = 101 + 10 = 111

Age of B = y + 7 = 10 + 10 = 20

Difference between their ages = 111 - 20 = 99

${\sf {\orange{\underline { The\: difference\: between\: their\: ages\: after\: seven\: years \:from \: now\: is \: 99 \: years }}}}$