last year Akhilbabu and Chanda Devi were the candidate in bakultala gram panchayat election. akhilbabu defeated chanda devi by 75. If 20% of the voter who have casted akhilbabu would have casted to chandadevi ,then chanda devi could be won by 19 votes. by forming sumultaneous equations let us solve and find out how many votes each of them had got.
Answers
Given :-
- Akhilbabu defeated chanda devi by 75.
- If 20% of the voter who have casted akhilbabu would have casted to chandadevi ,then chanda devi could be won by 19 votes.
To Find :-
- How many votes each of them had got ?
Solution :-
Let us assume that, Akhilbabu got total x votes and Chanda Devi got total y votes. (x > y . )
so,
→ x - y = 75 ------------ Eqn.(1)
also,
→ (y + 20% of x) - (x - 20% of x) = 19
→ {y + (x/5)} - {x - (x/5)} = 19
→ {y + (x/5)} - (4x/5) = 19
→ y - (3x/5) = 19
→ 5y - 3x = 95 ------------ Eqn.(2)
Multiply Eqn.(1) by (-3) and subtracting from Eqn.(2), we get,
→ (5y - 3x) - {(-3)(x - y)} = 95 - {(-3) * 75}
→ (5y - 3x) - (-3x + 3y) = 95 - (-225)
→ 5y - 3x + 3x - 3y = 95 + 225
→ 2y = 320
→ y = 160 .
putting value of y in Eqn.(1),
→ x - 160 = 75
→ x = 75 + 160
→ x = 235 .
Hence, Akhilbabu got total 235 votes and Chanda Devi got total 160 votes.
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