Question

5 The denominator of a fraction exceeds its numerator by 7. If two is added to the numerator
3 is subtracted from the denominator, the fraction becomes 3/5. Find the original fraction
5​

Answer 1

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

Given :

☞ Denominator ( D ) = N + 7

☞ Numerator ( N ) = 2 is added

☞ Denominator = 3 is subtracted

☞ Fraction = 3 / 5.

According to the question :

=> N + 2 / D - 3 = 3 / 5

=> 5 ( N + 2 ) = 3 ( D - 3 )( cross multiply )

=> 5N - 10 = 3D - 9

=> 5N - 3D = -9 - 10

=> 5N - 3D = 19

=> 5N = 3D - 19

Substituting ' D ' value :

=> 5N = 3D - 19. ( D = N + 7 )

=> 5N = 3 ( N + 7 ) - 19

=> 5N = ( 3N + 21 ) - 19

=> 5N - 3N = 21 - 19

=> 2N = 2

=> N = 2 / 2

=> N = 1.

Denominator :

=> D = N + 7

=> D = 1 + 7

=> D = 8.

☞ Therefore, The original

fraction is 1 / 8.