How many girls went home?

Question

There were 629 children in a festival. After 85 boys and two-thirds of the girls went home, the number of girls remaining is a fifth of the boys remaining. How many girls went home?

 

a. 88

b. 102

c. 136

d. 205

 

Answer 1

Let No.of total girls =x

No. of total boys =y

 

x+y=629   ___________ equation 1

 

total children went to home=85 boys + 2/3 x girls

 

remaining boys are  y-85

 

remaining girls are 1/5*(y-85)

 

85+ 2/3 x + y-85+ 1/5(y-85)=629

2/3 x+ y+y/5-85/5=629

2/3x+y+y/5-17=629

2/3x+y+y/5=646

 

LCM of denominator is 15

 

10x+15y+3y=9690

 

10x+18y=9690 _____________equation 2

 

y=629-x     from equation 1

 

substitute value of y in equation 2

 

10x+18(629-x)=9690

10x+11322-18x=9690

-8x=-1632

x=204

 

so total girls are 204

girls went to home is 2/3 rd of total girls

so 204* 2/3=136

 

so no.of girls went to home are 136

 

 

so answer is c) 136

Answer 2

Namita, awesome problem solving!