Percentage Part-3

In Continution to the previous notes...

Expenditure and consumption:

expenditure = price x quantity 

case -1 : when expenditure is constant 
then price and quantity are inversly proportional 
i.e

p ∝ 1/q

or 

q ∝ 1/p 

case -2 
when price constant 
exp. ∝ qunt 
 

case -3 
when quantity constant 
exp. ∝ price  

Question1 : If the price of milk increased by 25%, by how much per cent must Rahul decrease his consumption, so as his expenditure remains the same.
Solution: Let the price of milk is 20 Rs/ litre and Rahul consumes 1-litre milk.
Expenditure of Rahul = price × consumption
Now the price of milk is increased by 25%, so the new price is (125/100)× 20 = 25 Rs.
but his expenditure remains the same
So, new consumption × new price = old price × old consumption
      new consumption × 25 = 20 × old consumption
      new consumption  =(20/25)  × old consumption
      new consumption% = (20/25)× old consumption × 100
      new consumption% = 80% of old consumption
decrease in consumption = 20 %
Using above trick:  Given, price % is increased so sign will be (+) and consumption % will decrease.
Decrease in consumption =(25/125) × 100 = 20%

or 
              original : final  
price -       4        :      5 

Quantity - 5        :     4
=> (1/5) x 100 % = 20 %  

Question- 2  : If the price of milk decreased by 25%, by how much percent must Rahul increase his consumption, so as his expenditure remains the same.
Solution: Let the price of milk is 20 Rs/ litre and Rahul consumes 1-litre milk.
Expenditure of Rahul = price × consumption
Now the price of milk is decreased by 25%, so the new price is × 20 = 15 Rs.
but his expenditure remains the same
So, new consumption × new price = old price × old consumption
      new consumption × 15 = 20 × old consumption
      new consumption  =  (20/15)× old consumption
      new consumption% = (20/15)× old consumption × 100
      new consumption% = 133(1/3)% of old consumption
     increase in consumption = 33(1/3) %
Using above trick: given price % is decreased so sign will be (-) and consumption % will increase.
Increase in consumption = (25/75) x  100 = 33(1/3)%

OR 

              original : final  
price -       4        :      3 

Quantity - 3        :     4

(1/3) x 100% = 33 1/3%
 

Marks based questions

If the passing marks in an examination is R%. If a candidate scores S marks and fails by F marks,then

Maximum Marks =       

Question 3:A student has to score 30% marks to get through. If he gets 30 marks and fails by 30 marks, then find the maximum marks set for the examination ?
Solution:

Maximum Marks=100(30+30)/30=200 Marks

or

if student gets 30 marks and fail by 30 marks then passing marks for the student will be 60 
i.e

30% of total marks = 60 
=> 1% of total marks = 2 
100% of total marks = 200 

Question 4:

At an examination in which maximum marks are 500. K got 10% less than L, L got 25% more than M and M got 20% less than N. If K got 360 marks what percentage of marks was obtained by N ?

Solution:

Let marks obtained by N = x

M's marks = 0.80x

L's marks = 1.25 (0.80x)

K's marks = (0.90) (1.25) (0.80x) = 0.9x

But 0.9x = 360 ⇒ x = 400

Percentage of Marks obtained by N

= 400 x 100/500 = 80%

or by ratio and proportion 
  K  :   L   :   M    :   N 
 9   : 10       ---      ---

 ---     5   :   4        ---
 ---   ---       4     :    5
---------------------------- 

----------------------------

 K  :   L   :   M    :   N 
 9     10     10       10
 5       5      4         4
 4       4      4         5 

FINAL RATIO 
K      : L      : M      : N

180 : 200 : 160   : 200

marks of k = 360 i.e 180 unit = 360 marks 

200 units ( value of N ) = 200 x 2 = 400 

Distribution based Question:

Question 5: Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?

Solution:

Saving  = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400

= Rs. (50/100 * 60/100 * 70/100 * 18400)

= Rs. 3864.

or 

10 : 7 
 5 : 3 
 2 : 1 
-----------
100 : 21 
-----------

100 unit = 18400 
1 unit = 184 
21 unit = 184 x 21 
3864 rs 

 

Question 6:   Radha spends 40% of her salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If her savings at the end of a month are Rs. 1500, then her salary per month (in Rs.) is ?

Solution:

Assume the Total Salary = 100%

Expenditures:-

Food = 40%

House Rent = 20%

Entertainment = 10%

Conveyance = 10%

Total Expenditure = 80%

Savings = 100% - 80% = 20% ---------> 1500 Rs.

1% ---------> 1500 Rs./20 = 75 Rs.

100% ---------> 75 * 100 = 7500 Rs.