Question

Two numbers are in the ratio of 4 : 7. If 14 is added to each, they are in the ratio 5 : 7, then find the numbers?

• A. 20 and 35
• B. 12 and 21
• C. 16 and 28
• D. 15 and 18

Hint:

When working with ratios, use the method of setting up equations to find the unknown values.

Answer 1

The Correct Option is C

Let the two numbers be \( 4x \) and \( 7x \). When 14 is added to each, the new ratio is given by: \[ \frac{4x + 14}{7x + 14} = \frac{5}{7}. \] Cross multiplying: \[ 7(4x + 14) = 5(7x + 14) \quad \Rightarrow \quad 28x + 98 = 35x + 70 \quad \Rightarrow \quad 7x = 28 \quad \Rightarrow \quad x = 4. \] Thus, the two numbers are \( 4x = 16 \) and \( 7x = 28 \).