Question

30. Five years ago, the age of Sultan will three times that of Sadiq. Ten years later,
Sultan will be twice as old as Sadiq . How old are Sultan and Sadiq now?​

Answer 1

$\green{ \large{ \sf \rightarrow SOLUTION \leftarrow}}$

$\sf \: Let \: present \: age \: of \: Sadiq \: be(x) \\ \sf \: Present \: \: age \: \: of \: \: sultan \: \: is \: \: (y) \: \:$

$\large{ \sf \: 5 \: years \: ago} \rightarrow$

$\sf \: age \: of \: sadiq \: = x - 5 \: \: year \\ \sf \: age \: of \: sultan \: = y - 5 \: year$

$\large{ \sf \: According \: to \: question } \rightarrow$

$\sf \: age \: of \: sultan \: = 3( age \: of \: sadiq) \\ \implies\sf \: y - 5 = 3(x - 5) \: \: \: \: \: \: \: \: \: \\ \implies\sf y - 5 = 3x - 15 \: \: \: \: \: \: \: \: \: \\ \implies\sf y = 3x - 15 + 5 \: \: \: \: \: \: \: \: \: \\ \implies\sf y = 3x - 10 \: \: \: \: \: \: \: .. ..(i)$

$\large{ \sf \: 10\: years \: latter} \rightarrow$

$\sf \: age \: of \: sadiq \: = x + 10\: \: year \\ \sf \: age \: of \: sultan \: = y + 10 \: year$

$\large{ \sf \: According \: to \: question } \rightarrow$

$\sf \: age \: of \: sultan \: = 2(age \: of \: sadiq) \\ \implies\sf y + 10 = 2(x + 10) \\ \implies\sf 3x - \cancel{10 }+ \cancel{10} = 2x + 20 \\ \implies\sf 3x = 2x + 20 \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies\sf 3x - 2x = 20 \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies\sf x = 20 \: \: year \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf \: y = 3x - 10 \\ \implies\sf y = 3(20) - 10 \: \: \: \: \\ \implies\sf y = 60 - 10 \: \: \: \: \: \: \: \: \: \: \\ \implies\sf y = 50 \:year \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf present \: age \: of \: Sadiq \: \: \green{ \boxed{ \sf \: x = 20 \: year}}\\ \sf \: Present \: \: age \: \: of \: sultan \green{\boxed{y = 50 \: year}}\: \:$