Question

During an annual function, the participants were divided equally among two teams, A and B. The ratio of the number of boys to the number of girls in Team A is 2 : 3 and that in Team B is 3 : 17. What is the ratio of the number of girls to the number of boys participating in the function?​

Answer 1

The ratio of total participating girls to boys = 29:11

Step-by-step explanation:

• As we can see that Team A is having the ratio = 2:3

• So we have total number of participants = 2+3 = 5

• Similarly, In team B the total number of participants will be = 3+17 =20

• We can see that the participants are equally divided in both the teams, therefore Team A would have 20 participants, and the ratio of team A is 2:3 so the total number of participants in Team A = 8+12 =20
• Now we can calculate the ratio of total participants the team for girls to boys:

         $\textrm {TEAM A} \rightarrow 8 : 12\\\textrm {TEAM A} \rightarrow 3 : 17\\\\\\\textrm{for both} \rightarrow 11 : 29\\\\\textrm{addition of both the teams}$

So the ratio of total participating girls to boys = 29:11

Answer 2

Answer:

29:11

Step-by-step explanation:

Lets say there were P participants. They were equally divided into two teams. So number of participants per team will be P/2.

Now this P/2 participants in Team A contains certain number of boys and girls in the ratio 2:3. Lets assume a factor X which when multiplied 2 and 3 will give the number of boys and girls in Team A. The ratio can be written as 2X: 3X. The total number of participants in Team A is

2X+3X = P/2 or 5X = P/2

Similarly P/2 participants in Team B contain boys and girls in the ratio 3:17.  Lets assume a factor Y which when multiplied by 3 and 17 gives the number of boys and girls in Team B. The ratio can be written as 3Y: 17Y. The total number of participants in Team B is

3Y+17Y = P/2 or 20Y = P/2

Now since both are equal to P/2 we can write it as

5X = 20Y or X = 4Y

The first ration 2X:3X can now be written as 2*4Y : 3*4Y or 8Y:12Y

That means in Team A there are 8Y boys and 12Y girls. In Team B there are 3Y boys and 17Y girls. So there are 11Y boys and 29Y girls in the annual function.

So the ratio of girls: boys in the function is 29Y:11Y. or simply 29:11