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 124. What is the original number?
Answer:
917
- Let the numerator be x. According to the question, the denominator will be equal to x+8. The fraction will be xx+8.
- The new numerator is x−8, and the new denominator is x+8+7=x+15. The new fraction will become:x−8x+15.
- According to the question, x−8x+15=124. On cross multiplication we get: 24(x−8)=x+15⟹24x−192=x+15⟹23x=207⟹x=9
- Hence the original fraction will be equal to 99+8, or 917.