Mauritius
The denominator of a rational number is greater than its numerator by ^@8.^@ If ^@8^@ is subtracted from the numerator and ^@7^@ is added to its denominator^@,^@ the new number becomes ^@\dfrac { 1 } { 24 }.^@ What is the original number^@?^@
Answer:
^@ \dfrac { 9 } { 17 } ^@
- Let the numerator be ^@x.^@ According to the question, the denominator will be equal to ^@x + 8.^@ The fraction will be ^@ \dfrac { x } { x+8 } . ^@
- The new numerator is ^@x - 8,^@ and the new denominator is ^@x + 8 + 7 = x + 15.^@ The new fraction will become^@: \dfrac { x-8 } { x+15 } . ^@
- According to the question, ^@ \dfrac { x-8 } { x+15 } = \dfrac { 1 } { 24 }. ^@ On cross multiplication we get^@:^@ @^ \begin{align} & 24(x - 8) = x + 15 \\ \implies & 24x - 192 = x + 15 \\ \implies & 23x = 207 \\ \implies & x = 9 \end{align} @^
- Hence the original fraction will be equal to ^@ \dfrac { 9 } { 9+8 },^@ or ^@ \dfrac { 9 } { 17 } ^@.
