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1.  Two students appeared at an examination. One of them secured 9 marks more than the other and
 his marks was 56% of the sum of their marks. What are the marks obtained by them?

Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)=14 (2x + 9)
=>25x+225=28x+126

  =>3x=99

 => x = 33.
So, their marks are 42 and 33

 

2. A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges
 he had originally?

 60  420
 100 !

 700

3.  A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score
 did he make by running between the wickets?

 110    50
  100    !

 45(5/11) %

4.  In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were 
invalid. If the total number of votes was 7500, what was the number of valid votes that the other
 candidate got?

 7500*20/100=1500
6000*55/100=3300
6000-3300= 2700

5.  A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. 
The maximum marks are

 125+40=165
 33   165
 100   !
165*100/33=.500

6. A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately
 how much percent she saved in the transaction ?

Actual Price = Rs.25 + Rs.2.50 = Rs.27.5

Saving = Rs.2.5
 27.5    2.5
100       !

 9(1/11) %

7. A pipe X is 30 meters and 45% longer than another pipe Y. find the length of the pipe Y?

Length of pipe X = 30 meter

Given that pipe X is 45% longer than Y

Let the length of pipe Y = y

Then, Length of pipe X = y×(100+45)100⇒30=y×145100=>y=30×100145=6×10029=60029=20.68

8. On my sister’s 15th birthday, she was 159 cm in height, having grown 6% since the year  before. 
How tall was she the previous year ?

150*6/100=15
150 cm

9. Sumit got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith 
who took the same examination got 40% of the total marks and got 15 marks more than the passing
 marks. What were the passing marks in the examination?

The problem however, states that  Sumit got 15 marks more than the passing mark and got Sujith 10 marks 

less than the passing mark. Therefore, Paul has got 15 + 10 = 25 marks more than Peter. 'x' is the maximum 

mark and is equal to 250 marks.

10   25

100  !

=25*100/10=250

We know that Peter got 30% of the maximum marks.

Therefore, = 75 marks.

We also know that Peter got 10 marks less than the passing mark.

Therefore, the passing mark will be 10 marks more than what  got = 75 + 10 = 85.

10. 30% of the men are more than 25 years old and 80% of the men are less than or equal to  50 years
 old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentag
e of the football players are less than or equal to 50 years?

20% of the men are above the age of 50 years. 20% of these men play football. Therefore, 20% of 20% or 4% of the

 total men are football players above the age of 50 years.

20% of the men are football players. Therefore, 16% of the men are football players below the age of 50 years.

Therefore, the % of men who are football players and below the age of $50=\left(\frac{16}{20}\right)\times 100=$ 80%