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From a group of boys and girls, 14 girls leave first. Then the ratio of the number of girls to the number of boys becomes 1:2. After this, 43 boys leave the group. Now the boys and girls are equal in number. How many girls were there in the beginning?

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Answers

2014-11-09T10:53:48+05:30
Let the number of boys be x and  
Let the number of girls be y

Then , A.T.Q

1. y - 14   =  1
     x           2
By cross multiplication.

2y - 28 = x ----------------------------------1

2. x - 43   = 1
   y - 14      1

By cross multiplication 
x - 43 = y - 14

Putting the value of x from 1

2y -28 - 43 = y - 14

2y - y = -14 + 71
 
y = 57.

Putting the value of y in 1

2y - 28 = x

2( 57) - 28 = x
 
114 -28 = x
x= 86

Hence the number of boys = 86 and number of girls = 57.



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2014-11-09T11:20:50+05:30
From a group of boys and girls, 14 girls leave first. Then the ratio of the number of girls to the number of boys becomes 1:2. After this, 43 boys leave the group. Now the boys and girls are equal in number. How many girls were there in the beginning?
solution: -

            let the number of girls = x
             and  number of boys = y
                 According to question ,
                 After 14 girls left the group ,
                   x - 14 /y = 1/2 
                   or  2( x - 14 ) = y
                         2x - 28 = y  ................. (1st )

             After 43 boys left the group ,
                   x-14/y - 43 =1
                       x - 14 = y - 43
                       x  -  14 + 43 = y
                       x +29 = y  .......................... (2nd )
 Using 2nd in 1st , we get
                   2x - 28 = x +29
                   2x = x+29 +28
                   2x - x = 29 + 28
                   x = 57

Hence the number of girls in the beginning  were 57.

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