If 40 is added to a list of natural numbers, the average is increased

1.	If 40 is added to a list of natural numbers, the average is increased by 4. When 30 is added to the new list, the average of the numbers in the new list is increased by 1. How many number were in the original list ?1. 82. 53. 44. 6
Answer» Correct Answer - Option 3 : 4 Let there be n numbers in the original list and let their mean be y. Then, sum of n numbers = ny According to Question \(⇒ (ny+40)/(n+1)=y+4 ……(1 ) \) \(⇒(ny+40+30)/(n+2 )=y+5 ……(2 )\) On solving Eq 1 ny + 4n +y+4 = ny + 40 4n + y = 36× 5 ……(3 ) Similarly eq 2 5n + 2y = 60× 4 ……(4 ) On solving eq 3 and 4 by elimination y = 20 , n = 4

If 40 is added to a list of natural numbers, the average is increased by 4. When 30 is added to the new list, the average of the numbers in the new list is increased by 1. How many number were in the original list ?1. 82. 53. 44. 6

Answer» Correct Answer - Option 3 : 4

Let there be n numbers in the original list and let their mean be y.
Then, sum of n numbers = ny

According to Question

\(⇒ (ny+40)/(n+1)=y+4 ……(1 ) \)

\(⇒(ny+40+30)/(n+2 )=y+5 ……(2 )\)

On solving Eq 1

ny + 4n +y+4 = ny + 40

4n + y = 36× 5 ……(3 )

Similarly eq 2

5n + 2y = 60× 4 ……(4 )

On solving eq 3 and 4 by elimination

y = 20 , n = 4

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If 40 is added to a list of natural numbers, the average is increased by 4. When 30 is added to the new list, the average of the numbers in the new list is increased by 1. How many number were in the original list ?1. 82. 53. 44. 6

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