Question

Question 2 of 40
Each of the four parties A, B, C and D contested in all the seats in an election. Each seat was won by exactly one of the four parties. Party A
lost on 19 seats, Party B lost on 12 seats, Party Clost on 10 seats and Party D lost on 16 seats. What was the total number of seats being
contested in the election?​

Answer 1

Answer:

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Answer 2

Final Answer:

The total number of seats that are being contested in the election is 19.

Given:

The four parties A, B, C, and D contested all the seats in an election. Each seat was won by exactly one of the four parties.

Party A is said to lose 19 seats.

Party B is stated to lose 12 seats.

Party C also lost 10 seats.

Party D has lost 16 seats.

To Find:

The total number of seats that are being contested in the election is to be calculated.

Explanation:

The vital concepts necessary for the solution to this problem are as follows

• The number of seats lost by one of the four parties is actually won by the other three parties.
• The number of seats lost by a party is the difference between the total number of seats and the number of seats won by that party.

Step 1 of 3

As per the given statement in the problem, assume the following.

• The number of seats won by party A is a.
• The number of seats won by party B is b.
• The number of seats won by party C is c.
• The number of seats won by party D is d.

Step 2 of 3

Using the information in the given problem, deduce the following equations.

$b+c+d=19\;\;\;\;....(i)\\c+d+a=12\;\;\;\;....(ii)\\d+a+b=10\;\;\;\;....(iii)\\a+b+c=16\;\;\;\;....(iv)$

Step 3 of 3

In continuation with the above calculations derive the following.

$3(a+b+c+d)=19+12+10+16=57\\( a+b+c+d)=\frac{57}{3}=19\;\;\;\;...(v)$

Subtracting the first four equations from equation (v), the following is derived.

$\\ a=19 -19=0\\b=19 -12=7\\c=19 -10=9\\d=19 -16=3$

Therefore, the required correct answer is a total of 19 seats.

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