What is the value of (2x+3y), if mean of the following distribution is 54 ?

Class	0-20	20-40	40-60	60-80	80-100	Total
Frequency	7	11	x	9	y	50

Correct option is B

Given:

Given data for class and  frequancy

Mean of data = 54

Formula Used:

​$$Mean = \frac{\sum{x_i f_i}}{\sum{f_i}}$$​​

Solution:

​$$\sum{x_if_i} = 70 +330+50x+630+90y = 1030 +50x+90y$$​​

​$$\sum{f_i} =7+11+x+9+y =50$$​​

27 +x+y = 50

x+y = 23   ….(1)

​$$Mean = \frac{\sum{x_i f_i}}{\sum{f_i}}$$​​

​$$54= \frac{1030+50x+90y}{50}$$​​

1030+50x+90y = 2700

50x+90y = 2700-1030

50x+90y = 1670

Substituting the value of y from eq(1)

50x + 90(23-x) = 1670

50x+2070-90x =1670

40x=2070-1670

​$$x=\frac{400}{40}= 10$$​​

y= 23-10 = 13

The value of (2x+3y) = 20 + 39 = 59