FDPs

This topic has expert replies
User avatar
Master | Next Rank: 500 Posts
Posts: 167
Joined: Fri Mar 09, 2012 8:35 pm
Thanked: 39 times
Followed by:3 members

FDPs

by adthedaddy » Sat Aug 18, 2012 7:52 am
Last year, all registered voters in a country voted either for Party-A or for
the Party-B. This year, the number of Party-A voters increased 10%, while
the number of Party-B voters increased 5%. No other votes were cast. If the number of
total voters increased 8%, what fraction of voters voted Party-A this year?


Ans: 11/18

Please help solve this problem. Request to describe the detailed steps. I want to know the approach to solve such problems.
Source: — Problem Solving |

Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Tue Aug 14, 2012 10:58 am
Thanked: 1 times

by Yishai » Sat Aug 18, 2012 8:59 am
Hi Ad,
I plugged a number for the total voters last year and then formed an equation.
1. Plug 200 for the no. of voters in the 1st year
2. X for party A, (200-X) for party B
3. This year there are 216 voters (8% increase)
4. The equation after taking into account the increase in voters for each party is:
1.1X+1.05(200-X)=216
5. The fraction of voters for party A this year is 1.1X/216
6. Solve (4) and you'll get 11/18 after reducing the fraction.

I hope this helped,
Cheers

User avatar
Senior | Next Rank: 100 Posts
Posts: 94
Joined: Sat Mar 31, 2012 3:39 am
Location: Calcutta
Thanked: 8 times

by cypherskull » Sat Aug 18, 2012 9:56 am
Let a & b represent the number of votes received last year.

Therefore, the votes received this year becomes:

1.1a and 1.05b

Since the total votes this year increased by 8%, we get -

1.1a + 1.05b = 1.08(a+b)

Simplifying this, we get -

0.02a = 0.03b => 2a = 3b => b = 2a/3

The required fraction (for this year) would be -

1.1a/1.08*(a+b)

Replace the b = 2a/3 in the above equation. We get -

1.1a/1.08(a + 2a/3) => 1.1a/1.8a = 11/18 Answer.
Regards,
Sunit

________________________________

Kill all my demons..And my angels might die too!

User avatar
Master | Next Rank: 500 Posts
Posts: 167
Joined: Fri Mar 09, 2012 8:35 pm
Thanked: 39 times
Followed by:3 members

by adthedaddy » Sat Aug 18, 2012 10:36 am
Thanks folks. The explanation helped :-)