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In an election, 2% persons enrolled in the voter list did not participate and 500 votes were invalid. Two candidates A and B fought the election, and A defeated B by 200 votes. If 43% of the persons enrolled in the voter list casted their votes in favour of A, then what is the number of the total casted votes?
Let the total number of enrolled voters be ( x ).According to the problem:- 2% of enrolled voters did not participate, which means 98% did participate.- The number of valid votes cast would then be ( 0.98x - 500 ) (where 500 is the invalid votes).- A received 43% of the votes, so A's votes are ( 0.4Read more
Let the total number of enrolled voters be ( x ).
According to the problem:
– 2% of enrolled voters did not participate, which means 98% did participate.
– The number of valid votes cast would then be ( 0.98x – 500 ) (where 500 is the invalid votes).
– A received 43% of the votes, so A’s votes are ( 0.43 times (0.98x) ).
– B’s votes can then be calculated since A defeated B by 200 votes, which gives us the equation:
( text{Votes for A} = text{Votes for B} + 200 ).
We have:
[
text{Votes for A} = 0.43 times (0.98x)
]
[
text{Votes for B} = (0.98x – 500) – text{Votes for A}
]
Substituting B’s votes into A’s winning margin:
[
0.43 times (0.98x) = (0.98x – 500) – (0.43 times (0.98x)) + 200
]
Simplifying:
[
0.43 times (0.98x) + 0.43 times (0.98x) = 0.98x – 500 + 200
]
[
See less0.
P is two times more efficient than Q. P is able to complete a piece of work in 40 days less than Q. Working together, the whole number of days taken by them to complete the work is: (Round off to the nearest integer)
Let the work done by Q in one day be ( x ). Then, the work done by P in one day is ( 2x ).Let the number of days taken by Q to complete the work be ( d ). Therefore, the time taken by P to complete the work is ( d - 40 ).Since work is equal to the rate of work multiplied by the time taken, we can eqRead more
Let the work done by Q in one day be ( x ). Then, the work done by P in one day is ( 2x ).
Let the number of days taken by Q to complete the work be ( d ). Therefore, the time taken by P to complete the work is ( d – 40 ).
Since work is equal to the rate of work multiplied by the time taken, we can equate the total work done by both:
[
Q’s work = x cdot d
]
[
P’s work = 2x cdot (d – 40)
]
Since both complete the same piece of work, we have:
[
x cdot d = 2x cdot (d – 40)
]
Dividing both sides by ( x ) (assuming ( x neq 0 )) gives:
[
d = 2(d – 40)
]
Expanding and solving for ( d ):
[
d = 2d – 80
]
[
80 = d
]
Now that we have ( d ), the number of days Q takes to complete the work is 80 days. The number of days P takes is:
[
d – 40 = 80 – 40 = 40 text{ days}
]
Next, we can find the rate of work for Q (in terms of total work done):
See lessIn a race around a circular cycling track of 75 km, two cyclists are riding at a speed of 30 km/h and 25 km/h. After what time (in hours) will they meet at the point from where they started their journey?
To find the time at which the two cyclists meet at the starting point, we can use the concept of relative speed. 1. Speed of Cyclist A (faster cyclist): 30 km/h 2. Speed of Cyclist B (slower cyclist): 25 km/h3. Relative Speed: The difference in their speeds is 30 km/h - 25 km/h = 5 km/h.They will meRead more
To find the time at which the two cyclists meet at the starting point, we can use the concept of relative speed.
1. Speed of Cyclist A (faster cyclist): 30 km/h
2. Speed of Cyclist B (slower cyclist): 25 km/h
3. Relative Speed: The difference in their speeds is 30 km/h – 25 km/h = 5 km/h.
They will meet at the starting point when the faster cyclist covers a distance that is a multiple of the circular track’s circumference, in this case, 75 km.
To find the time it takes for the faster cyclist to cover the track’s distance:
– Time = Distance / Speed
Considering the complete lap required to meet at the starting point:
– Time for Cyclist A to complete one lap: ( frac{75 text{ km}}{30 text{ km/h}} = 2.5 text{ hours} )
– Time for Cyclist B to complete one lap: ( frac{75 text{ km}}{25 text{ km/h}} = 3 text{ hours} )
Now, we look for the least common multiple (LCM) of their times to determine when they will both be back at the starting point:
– LCM of 2.5 hours and 3 hours can be calculated as follows:
– Convert to fraction: 2.5 = (
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The Khudai Khidmatgars, also known as the Red Shirts, were organized under the leadership of Bacha Khan, who was also known as Abdul Ghaffar Khan.
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