The ratio between two consecutive natural numbers (in ascending order) is reversed if seven is added to the first number and four is added to the second number. The sum of the two consecutive numbers is _______.
Solution
✅ Correct Option: 1
Let the consecutive natural numbers be $n$ and $n+1$. After adding 7 to the first number and 4 to the second, the ratio becomes the reverse of the original ratio: $\dfrac{n+7}{n+5}=\dfrac{n+1}{n}$ Cross-multiplying gives $n(n+7)=(n+1)(n+5)$. $n^2+7n=n^2+6n+5$ $n=5$ The numbers are 5 and 6, so their sum is $11$.