## Percentage Sheet

In this forum, please discuss the questions appearing in the QA class sheets :especially the practice and the DS questions at the end of the sheet.

### Percentage Sheet

QCS-7 Question-19

Assume the total people who are on the voters list to be "x"
Number of people who voted = x - 10% of x = 0.9 x ( Given in the question that 10% of the people on the voter's list did not vote.
Number of legal votes = 0.9x -60 ( 60 votes were declared as invalid)

Winner was supported by 47% of the people on the voting list = Number of votes won by the winner (W) = 0.47 x
Losers votes (L) = 0.9x -60 - 0.47x = 0.43 x - 60

Winning margin is equal to the number of votes of the winner less the number of votes won by the loser

Winning margin = 308 = 0.47x -( 0.43 x - 60)

=> 308 = 0.04x +60 => 248 = 0.04x or x = 6200
But the question wants us to find out the total number of legal votes = 0.9x -60 = 0.9 (6200) -60 = 5520

Posts: 228
Joined: Wed Feb 13, 2013 5:51 am

### Re: Percentage Sheet

QCS-7 Question 16

Assume initial price of eggs to be Rs p per egg

Price after 40% reduction = p - 40% of p = 0.6 p

Now the basic equation for the above should be

q2 -q1 = 48 ( q1 is the initial quantity bought at the normal price and q2 is the price after the price decrease)

The relation between expenditure, Price and Quantity is => Expenditure = Price x Quantity
Or E = P x Q OR Q = E/P

q1 = 1/p (Note that the man has spent Re 1 in buying the eggs)
q2 = 1/0.6p ( The expenditure remains the same but the price reduces to 0.6p)

1/(0.6p) -1/p = 48

On solving for p, we get p =1/72

Thus we have original price per egg. THEREFORE, the reduced price per egg = 0.6 x 1/72 = 1/120

Reduced price per dozen = ( 1/120) x 12 = 1/10 or 10 paise

Alternate approach:

If the price reduces by 40%, whatever quantity we bought earlier for Re 1 would now be available for 0.6 Rs

Therefore the extra 48 eggs which the man is able to purchase must have been purchased for 1-0.6 = 0.4 Rs

Reduced price per egg = 0.4/48 = 1/120 per egg

Reduced price per dozen = 1/120 x 12 = 1/10

Posts: 228
Joined: Wed Feb 13, 2013 5:51 am

### Re: Percentage Sheet

QCS-7 Question 17

Again we can assume that Manmohan's salary is Rs x

Savings = 20% of Rs x = Rs 0.2x

Expenditure = Rs x - Rs 0.2x = Rs 0.8x

Expenditure increases by 20 % therefore the new expenditure = 0.8x + 20% of 0.8x = 0.96x

His savings = x - 0.96x = 0.04x => 0.04x = 20 or x = Rs 500

Posts: 228
Joined: Wed Feb 13, 2013 5:51 am

### Re: Percentage Sheet

QCS-7 QNO-26

Salary = Hourly wage (W) x Number of hours worked (H)

Thus the salary initally = Rs 500 = W x H ........(1)

Hourly wages of the worker becomes W + 20% OF W = 1.2W and the Number of hours = H- 20% OF H = 0.8H

nEW WAGE = 1.2W x 0.8H = 0.96 (WxH)
Putting the value of W xH from 1 we have New wage = 0.96 x 500 = Rs 480