In a college election, if 15% of the students didnot vote and winning candidate got 62.5% of votes casted, then a candidate won by 3400.Find the number of students
Answers
Step-by-step explanation:
Given :-
In a college election, if 15% of the students didnot vote and winning candidate got 62.5% of votes casted, then a candidate won by 3400.
To find :-
Find the number of students?
Solution :-
Let the students in a college be X
The number of students did not vote in the election = 15% of the students
=> 15% of X
=> 15% × X
=> (15/100) ×X
=> (3/20)×X
=> (3×X)/20
=> 3X/20
Remaining students =X-(3X/20)
=> (20X-3X)/20
=> 17X/20
Number of students who cast their votes = 17X/20
Number of votes got by winning candidate = 62.5% of the votes casted
=> 62.5% of 17X/20
=> 62.5% × 17X/20
=> (62.5/100)×(17X/20)
=> (625/1000)×(17X/20)
=> (5/8)×(17X/20)
=> (5×17X)/(8×20)
=> 17X/(8×4)
=> 17X/32
Remaining votes he did not get = (17X/20)-(17X/32)
=> 17X[(1/20)-(1/32)]
LCM of 20 and 32 is 160
=> 17X(8-5)/160
=> 17X(3/160)
=>51X/160
The number of votes the winning candidate won by 3400
=> Winning candidate's votes - Losing candidate's votes = 3400
=> (17X/32) - (51X/160) = 3400
LCM of 32 and 160 = 160
=> [ (17X×5)-(51X×1)]/160 = 3400
=> (85X-51X)/160 = 3400
=> 34X/160 = 3400
=> 34X = 3400×160
=> X = 3400×160/34
=> X = 100×160
=> X = 16000
Therefore, X = 16000
Answer:-
The tot number of students in the college is 16000