Priyanka,
Is this a complete question? It reads exactly of the boys and exactly of the girls??

Here is the correct question

On a Soccer team consisting of 21 children, some of which are boys and some of which are girls,exactly 2/3 of the boys and exactly 1/3 of the girls attended the end of the season pizza party.What is the greatest number of children on team who could have attended the party?

Kindly check before posting!

Thanks

let the no of boys be B and the no of girl be G.

B+G = 21.

2/3 * B + 1/3 * G should be maximum.

that means B and G should be multiples of 3.

possibilities are (B,G)==>: (3,18), (6,15), (9,12),(12,9),(15,6), (18,3).

For the sum 2/3*B+1/3 *G to be maximum B should have the highest value possible which is 18 and G will be 3 then:

2/3*18 + 1/3*3 = 12+1 = 13

Let x be total number of boys

then, 21-x = total number of girls

total number of boys attended the party = 2x/3
total number of girls attended the party = (21-x)/3

Since 2/3 boys and 1/3 girls attended the party, to find out the greatest number of people attended the party we have to find the greatest number of boys.

Just plugin the answer choices to get the answer.

2x/3 + (21-x)/3 = 13

x= 18, 21-x = 3


Hope this helps.

Since 2/3 is a bigger fraction than 1/3, so maximize the number of boys in the team keeping the number of girls divisible by three.

18 boys and 3 girls will be the first and the correct split.

Therefore 2/3*18 + 1/3*3 = 13 is the greatest number of children on the team who attend the party.