Two numbers are in the ratio of 3 : 7. If 11 is subtracted from each, the ratio between the numbers becomes 7 : 20. Find the smaller number.

The correct answer is 39.

Step 1: Represent the numbers using a variable.

Given that the ratio of two numbers is 3 : 7, let the two numbers be $3x$ and $7x$, where $x$ is a common multiplier.

The smaller number is $3x$ and the larger number is $7x$.

Step 2: Formulate the equation from the given condition.

If 11 is subtracted from each number, the new numbers become $3x-11$ and $7x-11$.

The ratio of these new numbers is given as 7 : 20. Writing this as an equation:

$\frac{3x-11}{7x-11}=\frac{7}{20}$

Step 3: Solve for $x$.

Cross-multiplying both sides gives:

$20(3x-11)=7(7x-11)$

Expanding the expressions on both sides:

$60x-220=49x-77$

Rearranging terms to group like terms together:

$60x-49x=220-77$

$11x=143$

Dividing both sides by 11:

$x=13$

Step 4: Find the smaller number.

Substitute $x=13$ back into the expression for the smaller number ($3x$):

$\text{Smaller number}=3\times 13=39$

Therefore, the smaller number is 39.