1-In a gram panchayat meeting, 1000 people on a resolution with 10 % of the votes being invalid. After some discussion 1000 people voted again. This time there were 20% invalid votes. The opponents were increased by 50% while the motion was now rejected by a majority, which is 300% more than it was formerly passed by. How many people voted against the resolution before the discussion? (a) 700 (b) 600 (c) 500 (d) 400 (e) None of these
Answers
Answer:
Option (d) 400
Step-by-step explanation:
10% of 1000 = 100
Therefore, first time, the no. of valid votes = 1000 - 100 = 900
Let the no. of people who voted against the resolution = x
Then the no. of people who voted for the resolution = 900 - x
The motion was passed by = 900 - x - x = 900 - 2x
When they voted again after discussion, 20% votes were invalid
Thus total valid votes = 1000 - 20% of 1000
= 1000 - 20 × 1000/100
= 1000 - 200
= 800
50% increase in x = x + (50/100) × x
= x + x/2
= 3x/2
No. of people who voted for = 800 - 3x/2
Motion was rejected by = 3x/2 - (800 - 3x/2)
= 3x - 800
Again,
The motion was rejected by = (900 - 2x) + (900 - 2x) × 300/100
= (900 - 2x) + (900 - 2x) × 3
= 4(900 - 2x)
Thus,
3x - 800 = 4(900 - 2x)
⇒ 3x - 800 = 3600 - 8x
⇒ 11x = 4400
⇒ x = 4400/11 = 400
Hope it helps.
Answer:
400 is the correct answer