Question

The sum of three numbers is 1600. The second number and the third number are in the ratio 11:18. While the first number and the third number are in the ratio 1:6. The second number is:

• A. 500
• B. 850
• C. 550
• D. 880

Hint:

When dealing with ratios, express the unknowns in terms of a common variable (such as \( z \)) and then substitute into the sum or other relationships.

Answer 1

The Correct Option is C

Let the three numbers be \( x \), \( y \), and \( z \), where: - The sum of the numbers is \( x + y + z = 1600 \) - The second and third numbers are in the ratio 11:18, so: \[ \frac{y}{z} = \frac{11}{18} \quad \Rightarrow \quad y = \frac{11}{18}z \] - The first and third numbers are in the ratio 1:6, so: \[ \frac{x}{z} = \frac{1}{6} \quad \Rightarrow \quad x = \frac{1}{6}z \] Now, substitute \( x = \frac{1}{6}z \) and \( y = \frac{11}{18}z \) into the sum equation: \[ x + y + z = 1600 \] \[ \frac{1}{6}z + \frac{11}{18}z + z = 1600 \] To simplify, find a common denominator: \[ \frac{3}{18}z + \frac{11}{18}z + \frac{18}{18}z = 1600 \] \[ \frac{32}{18}z = 1600 \] \[ z = \frac{1600 \times 18}{32} = 900 \] Now, substitute \( z = 900 \) into the equations for \( x \) and \( y \): \[ x = \frac{1}{6} \times 900 = 150 \] \[ y = \frac{11}{18} \times 900 = 550 \] Thus, the second number is \( y = 550 \).