Percentage Question - math aptitude

Q-:1
In presidency college two candidates contested a presidential election. 15% of the voters did not vote and 41 votes were invalid. The elected contestant got 314 votes more than the other candidate. If the elected candidate got 45% of the total eligible votes, which is equal to the no of all the students of the college . the individual votes of each candidate are - :

Solution-:

let total number of voters = x
total votes = 85x/100
total valid votes= 85x/100 - 41
number of votes winner get = 45x/100
number of votes loser get =
45x/100 - 314
total number of valid votes = number of votes winner get + number of votes loser get
=> 85x/100 - 41= 45x/100 + 45x/100 - 314
=> 85x - 4100 = 90x - 31400
=> 5x = 27300
=> x = 5460
total votes = 5460
votes of winner = 45% of 5460
= 45* 5460/100
= 2457
votes of loser = 2457-314 = 2143



Q-2


A group of students prepared stuffed toys as part of their group activity. They spent Rs. 100 on velvet, Rs 5 on thread and needle and Rs. 27 on miscellaneous items on each toy. They made 50 toys, 50% of which were purchased by force by some senior students causing them a loss of 50%. At what % profit should they sell the remaining toys so as to gain 50% on their total cost?

a) 100%
b) 150%
c) 75%
d) 125%
e) None of these

Ans-:

Total cost =100+27+5=132
Total cost price=132×50= 6600
let % of profit required to sell the rest 25 toys = x %
(3300- 3300*50/100)+(3300 + 3300*x/100)= 6600 + 6600* 50/100
=> 3300(1-1/2+1+x/100)= 6600(150/100)
=> 3/2 + x/100= 2 (150/100)
=> 300/2 + x = 2*150
=> 150 + x = 300
=> x=150%


Q-3 -:


Jamila sold a table and chair for rs 1050 thereby making a profit of 10% on table and 25% on chair.If she had taken a profit of 25% on table and 10% on chair she would have got rs 1065. Find the cost price of each.

Ans - :

Let the cost price of the table be Rs x and the cost price of the chair be Rs y.
The selling price of the table, when it is sold at a profit of 10% = Rs x + 10x/100 = 110x / 100

The selling price of the chair when it is sold at a profit of 25% = Rs y + 25y/100 = 125y / 100

So, 110x / 100 + 125y / 100 = 1050    ... (1)

When the table is sold at a profit of 25%, its selling price = Rs (x + 25x/100) = Rs 125x / 100

When the chair is sold at a profit of 10%, its selling price = Rs (y + 10y/100) = Rs 110y / 100

So, 125x / 100 + 110y / 100 = 1065   ... (2)

Solve (1) and (2), we get
x = 500 and y = 400

Hence. the cost price of the table is Rs 500 and the cost price of the chair is Rs 400.