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There are 200 members in a library. The average age of male members is 29 yrs and that of the female members is 24 yrs. If the average of all the members together is 26 yrs, What is the number of females members in the library? 

There are 200 members in a library. The average age of male members is 29 yrs and that of the female members is 24 yrs. If the average of all the members together is 26 yrs, What is the number of females members in the library?  Correct Answer 120 

GIVEN:
Total members = 200

Average age of males = 29 yrs

Average age of females = 24 yrs

Average age of all members = 26 yrs

FORMULA USED:

Average = Sum of observations/total number of observations

CALCULATION:

Let the numbers of females be x

∴ Males = 200 - x

Total age of males = 29 (200 - x)

Total age of females = 24 x

A.T.Q

/200 = 26

24x - 29x + 29 × 200 = 26 × 200

5x = 3 × 200

x = 120

∴ There are 120 females.

ALTERNATE SOLUTION:

                           Males                       Females
Average age -       29                               24

 

Average of all-                       26

 

Number (ratio)-       x                                  y

x = 26 - 24 = 2 ratio

y = 29 - 26 = 3 ratio

A.T.Q

5 ratio = 200

3 ratio = 200/5 × 3 = 120

∴ There are 120 females.

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