Two numbers are in the ratio 9:7. If 14 is subtracted from each, the ratio becomes 7:5. Then the numbers are

Correct option is C

Given:

1. Two numbers are in the ratio 9:7.

2. After subtracting 14 from each number, the ratio becomes 7:5

Formula Used:

1. Represent the numbers as 9x and 7x based on the given ratio.

2. After subtracting 14 from each:

​$$\frac{9x - 14}{7x - 14} = \frac{7}{5}$$​

3. Solve for x to find the numbers:

​$$9x - 14 = \frac{7}{5} (7x - 14)$$​

Solution:

1. Expand the equation:

​$$9x - 14 = \frac{7}{5} (7x - 14)$$​

Multiply through by 5 to eliminate the fraction:

5(9x - 14) = 7(7x - 14)

45x - 70 = 49x - 98

2. Simplify the equation:

45x - 49x = -98 + 70

-4x = -28

x = 7

3. Substitute x = 7 into 9x and 7x to find the numbers:

​$$9x = 9 \cdot 7 = 63$$​

​$$7x = 7 \cdot 7 = 49$$​

Final Answer:

The numbers are **63** and **49**.