Country P’s Olympic Committee is determining how much

[abhisheks901]

Country P’s Olympic Committee is determining how much sponsorship money it needs to raise in order to cover its expenses in helping athletes train for and travel to next summer’s Olympic Games. There are four possible sources of funding: government grants, income from television rights, team sponsorships, and individual endorsement deals. The Committee’s task is to determine how to maximize funding from the latter three sources, in order to send as many athletes as possible to the Games, while minimizing the drain on government funding. Government funding is provided only when the team is unable to fully fund its activities.

A small number of the highest-profile athletes have secured individual endorsement deals; this money, however, belongs to that athlete alone and any such athletes are removed from the team funding calculations. An individual team is considered underfunded if its funding (not including government sources) covers less than 95% of the team’s expected expenses. Any surplus funding from TV rights or team sponsors reverts to the Olympic Committee and may be reallocated among other teams. The government will then provide funding to match up to 5% of team expenses or the amount needed to reach 100% funding, whichever is smaller.

Country P’s athletes are split into 9 primary teams. For each team, the table lists expected funding from TV rights and team sponsors as well as the percentage of its own expenses that a team is anticipated to be able to cover from TV rights and team sponsors. In addition, the table indicates the maximum possible level of government funding. All monetary amounts are in thousands.

Team TV rights ($) Team Sponsors ($) Percent funded (%) Government ($)
Basketball 400 250 82 40
Boxing 130 185 92 17
Equestrian 175 415 68 43
Gymnastics 1,100 890 115 —
Soccer 1,800 1,300 126 —
Swimming 770 500 97 39
Tennis 850 330 96 49
Track & Field 1,000 345 103 —
Volleyball 100 130 86 13


For each of the following statements, all of which refer to the 9 teams discussed in the prompt, select Yes if the statement can be shown to be true using the information provided. Otherwise, select No.

Yes No
More than 50% of the teams are underfunded.
The government will not need to pay the maximum amount of funding that it has made available.
The government funding allocated to the equestrian team is more, as a percentage of total funding needed by that team, than is the government funding allocated to the basketball team.

My query is related to statement 2 and 3.

1) statement 2 : here surplus of teams is more than that of deficit of other 6 teams. so we concluded that yes, government will not need to pay the maximum amount of funding that it has made available.
but if suppose deficit is more than the surplus. then how do we calculate whether government will need to pay maximum funding that is made available by it?

2) statement 3: funding needed by equestrian team is $ 277.64 thousand and government funding available is $ 43 thousand. and
government funding as a percentage of total fund needed is 43/277.64 =15.48%.

whereas for basketball team fund needed $142.68 thousand. and funding available is $40 thousand.
government funding as a percentage of total fund needed is 40/142.68 = 28.03%.

i think in this way correct answer will be found.

[Sage Pearce-Higgins]

1) statement 2 : here surplus of teams is more than that of deficit of other 6 teams. so we concluded that yes, government will not need to pay the maximum amount of funding that it has made available.
but if suppose deficit is more than the surplus. then how do we calculate whether government will need to pay maximum funding that is made available by it?

We need to look in the information given for anything relating to amount of money that the government has made available. In the article we're told that "The government will then provide funding to match up to 5% of team expenses" implying that this is the maximum funding the government has available. Although it's worded in a confusing way (deliberately, of course), the question is really just asking if there is any team that is not underfunded. So long as at least one team is funding itself above 95%, then the government won't be paying the maximum.

2) statement 3: funding needed by equestrian team is $ 277.64 thousand and government funding available is $ 43 thousand. and
government funding as a percentage of total fund needed is 43/277.64 =15.48%.
whereas for basketball team fund needed $142.68 thousand. and funding available is $40 thousand.
government funding as a percentage of total fund needed is 40/142.68 = 28.03%.

It looks like you did some complicated calculations here, working out that, for the basketball team the TV rights and team sponsors funding of $650,000 constitutes 82% of the team budget, and a similar calculation for the equestrian team. However, an easier route is to see that, since both teams are "underfunded" (i.e. making less than 95% of their budget), the government funding will be 5% in both cases.