If the average (arithmetic mean) of x, y, and 20 is 10 greater than th

Question

If the average (arithmetic mean) of x, y, and 20 is 10 greater than the average of x, y, 20, and 30, what is the average of x and y?

A. 40
B. 45
C. 60
D. 75
E. 95

Lampard42 · Answer

(x+y+20)/3=10+(x+y+20+30)/4
(x+y+20)/3=(x+y+90)/4 Solve it to arrive at x+y=190;

average of x and y is sum of (x+y)/2 = 95 IMO E

CareerGeek · Answer

average (arithmetic mean) of x, y, and 20 is 10 greater than the average of x, y, 20, and 30
--> (x + y + 20)/3 = (x + y + 20 + 30)/4 + 10
Multiply by 12 on both sides
--> 4*(x + y + 20) = 3*(x + y + 20 + 30) + 120
--> 4*(x + y) + 80 = 3*(x + y) + 150 + 120
--> 4*(x + y) - 3*(x + y) = 270 - 80
--> x + y = 190

Average of x & y = (x + y)/2 = 190/2 = 95

IMO Option E

Pls Hit Kudos if you like the solution

TheNightKing · Answer

I went through options. 
A. x+y=80. Sum of x+y+20 is 100. Not divisible by 3. Ignore.
Same approach for B,C and D.
Only E Works out.

Kudos if you like it

Archit3110 · Answer

given
x+y+20/3 = x+y+50/4 + 10
solve for x+y = 190
so avg ; x+y ; 95
IMO E

Kimberly77 · Answer

Hi  Dillesh4096 , how did you get 120 and not 30 in this calculation after multiply by 4 ? Thanks

--> 4*(x + y + 20) = 3*(x + y + 20 + 30) + 120

BrushMyQuant · Answer

Theory

➡ Average = Sum of all the Values / Total Number of Values 
 ➡ Sum of All the values = Average * Total Number of Values

The average (arithmetic mean) of x, y, and 20 is 10 greater than the average of x, y, 20, and 30

Average of x, y, and 20 =  \frac{Sum}{3}  =  \frac{x + y + 20}{3}  =  \frac{x + y + 20}{3}

Average of x, y, 20 and 30 =  \frac{Sum}{4}  =  \frac{x + y + 20 + 30}{4}  =  \frac{x + y + 50}{4}

Average of x, y, and 20 = 10 + Average of x, y, 20 and 30 (given)

=>  \frac{x + y + 20}{3}  = 10 +  \frac{x + y + 50}{4}

Multiplying both the sides with 3*4 = 12 we get

=> 12 *  \frac{x + y + 20}{3}  = 12* (10 +  \frac{x + y + 50}{4}  )
=> 4 *(x + y + 20) = 120 + 3 * ( x + y + 50)
=> 4x + 4y + 80 = 120 + 3x + 3y + 150
=> 4x - 3x + 4y - 3y = 120 + 150 - 80 = 190
=> x + y = 190

The average of x and y

Average of x and y =  \frac{Sum}{2}  =  \frac{x + y }{2}  =  \frac{190}{2}  = 95

So,  Answer will be E .
Hope it helps!

Watch the following video to Learn the Basics of Statistics

https://www.youtube.com/watch?v=Cvy_HHw4KIs

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