some mathematics on percentage

problem

In an examination total students appeared are 40% girls and rest boys. Now 80% of the boys and 60% of the girls has succeeded in examination. How many % of the total have failed in the examination.


Solution:
When 40 % are the girls , so 60 % are boys. { In totality it is 100%}

When the answer is asking in % number, let us assume that total no os girls and boys are 100.

Now what is happening that out of 60 boys, 80% of the boys have passed.

No of boys have passed is  =  60* 80/100 = 48 No of boys or 48 % of boys have passed.
No of girls passed is =  40* 60/100 = 24 % of the girls have passed.

so  no of boys and girls failed = 100 - (48 + 24) = 28%

Other problem

In a school 83 % of students passed in mathematics, 79% students passed in English, 75% students passed in both the subjects and if total of students failed is 26. Find the total no of students.

Solution
83% or 83 no of students passed in mathematics.

So students passed in mathematics but failed in english  = 83- 75= 8%

Similarly students passed in english but failed in mathematics = 79-75= 4%

So the students who have passed in one subject and both subjects are 75 +4+8= 87%

and students failed 100- 87= 13%

Now 13% of the total students are 26 


Total no of students are  26* 100/13 = 200 nos. 



Aklbert buys 4 horses and 9 cows for Rs. 56,00000.00 . If he sells the horses at 10 % profit and cows with 20 % profit , then he earns a total profit of Rs.60000.00 . The cost of the horse and the cows.


Solution:

4x  + 9y =  5600000.________ (1) 

4* (x+ 10/100*x) + 9 * (y+ 20/100 *y) = 56000000 + 600000_________(2)



Another problem in percentage

A person gives 12 % additional discount on the discounted price after giving an initial discount on 20 % .If the final sale price is Rs. 5400.00 what it is labelled  price?


Let us start the math backwardly.

Final sale price is Rs. 5400.00 
He gave additional discount of 12 %

Before giving the discount price was Rs. 5400.00 + 12 % of 5400= Rs 6048.00
This price is already a discounted one by 20%

The price will be adding this discount =  6048 + 20% of 6048

= 6048 + 20/100 * 6048
=7257.60

the actual price before the discounting was  Rs. 7257.60   


another problem  SBI PO 2000

a shopkeeper sells 25 articles at Rs. 45 per article after giving 10 % discount and earns 50 % profit. If the discount is not given the profit gained ?

No of articles does not bear any significance in percentage computation as all are computed in 100 

At Rs. 45  he earns 50 % profit.

So his cost price is = Rs 45 - (50/100)45 =Rs. 22.5  

Now at Rs. 45 he gave 10 % discount , if he did not give the discount price will be  45 + (10/100)*45 = Rs.49.50

Now at cost price of Rs 22.50 , selling price is Rs. 49.50

Profit=  49.50 -22.50 =Rs.27.00 

profit percentage= 27/22.50 *100

A shopkeeper sold sarees  at RS 266 each after giving 5 % discount on labelled price . Had he not given the discount , he would have earned a profit of 12 % on the cost price . What was the cost price. (sbi po 1999)

If labelled price is X then  5% discount of Rs X is 266

x- (5/100)*x = 266
or 0.95 x = 266
or x = 280

Now the condition is the at Rs 280 he will earn 12 % profit above cost price

let cost price be Rs. y 
Then,  y + 12 % y =  280
or y + 0.12 Y = 280
or 1.12 Y =280
or y= Rs. 250