The ratio of the average of two numbers to one of the numbers is 2 : 3. What is the ratio of the larger number to the smaller number?

Correct option is D

✔ Step 1: Let the two numbers be x and y
· Assume x>y
✔ Step 2: Average of the two numbers
· Average=x+y/2​
✔ Step 3: Given condition
· Average/y=2/3 ​
· So, x+y/2/y=23 ​
✔ Step 4: Solve the equation
x+y/2y=2/3⇒x+y/y=4/3⇒x+y=4y/3⇒x=4y3−y=y/3 ​
Oops! Correction in approach:
Better to set x=a, y=b and use the given:
(a+b)/2/b=2/3⇒a+b/2b=2/3⇒a+b/b=4/3⇒a+b=4b/3⇒a=4b/3−b=b/3 ​
Still not matching—let’s cross-multiply correctly:
a+b/2b=2/3⇒3(a+b)=4b⇒3a+3b=4b⇒3a=b⇒a:b=1:3
Actually, bigger number is b, and smaller is a
So, larger : smaller = b : a = 3 : 1
✔ Final Conclusion
· Ratio of larger number to smaller number is 3 : 1