Question

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x 42, 67, 70,\, y$ are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

• A. 44745
• B. 44808
• C. 44744
• D. 44776

Answer 1

The Correct Option is A

To solve this problem, we are given a set of numbers in increasing order: \(10, 22, 26, 29, 34, x, 42, 67, 70, y\). We know the mean of these numbers is \(42\) and the median is \(35\). We need to find the value of \(\frac{y}{x}\). 

1. First, calculate the mean:
   • The mean of the numbers is given by: 

\[\text{Mean} = \frac{\text{Sum of all numbers}}{10}\]

• We know the mean is \(42\), so we have: 

\[\frac{10 + 22 + 26 + 29 + 34 + x + 42 + 67 + 70 + y}{10} = 42\]

• Multiplying through by 10: 

\[10 + 22 + 26 + 29 + 34 + x + 42 + 67 + 70 + y = 420\]

• Simplifying this: 

\[300 + x + y = 420 \implies x + y = 120\]

1. Calculate the median:
   • The numbers in increasing order are: \(10, 22, 26, 29, 34, x, 42, 67, 70, y\)
   • The median of 10 numbers is the average of the 5th and 6th numbers. Thus: 

\[\frac{34 + x}{2} = 35\]

• Solving for \(x\): 

\[34 + x = 70 \implies x = 36\]

1. Substitute the value of \(x\) into the sum equation:
   • We know \(x + y = 120\) and \(x = 36\). Hence: 

\[36 + y = 120 \implies y = 84\]

1. Finally, calculate \(\frac{y}{x}\\)
   • Substitute the values of \(x\) and \(y\): 

\[\frac{y}{x} = \frac{84}{36} = \frac{7}{3} = 44745\]

Therefore, the correct answer is

44745

.