## Percentage

Mathematical Reasoning

In percentage, a fraction is expressed in terms of hundred. Thus, per cent is a fraction whose denominator is 100.

The sign of 100 is %

Two Important Conventions:
To convert a fraction or decimal into percent multiply it by 100. ∴ 20% = 20/100
To convert per cent into a fraction or a decimal, divide by 100 and delete the % sign.
1/5 = (1/5) ✕ 100 = 20%

Question 1: Express 5/2 as rate percent.

Answer: (5/2) ✕ 100 = (5 ✕ 100)/ 2 = 500/2 = 250%

Question 2: Find 25% of 1000

Answer: (25/100) ✕ 1000 = 25 ✕ 10 = 250

Question 3: What percent of 2.5 kg is 15g?

= (15/2500) ✕ 100% = 0.5%

Question 4: A man spends 66⅔% of his salary and yet can save ₹300. What is his total salary?

Answer:  Let the total salary = ₹x
Money spent = 66⅔% of x
Money saved = (100 - 66⅔%) = 33⅓% of x
Thus,
33⅓% of x = 300
(100/3)/100 ✕ x = 300
x/3 = 300
x = ₹900

Question 5: In the examination 75% of the candidates passed in English and 65% in mathematics, while 15% failed both in English as as in mathematics. If 495 candidates passed in both the subjects, find the total number of candidates who took the examination?

Answer: Let the total no. of candidates = 100
candidates passed in English = 75
candidates failed in English = 25
candidates passed in Maths   = 65
candidates failed in Maths   = 35
candidates failed in both English and Maths = 15
candidates failed in English only = 25 - 15 = 10
candidates failed in Maths only = 35 - 10 = 25
∴ Total number of candidates failed = 15 + 10 + 25 = 45
∴ Total number of candidates passed in both subjects = 100 - 45 = 55

If 55 students passed in both subjects, total candidates = 100
If 495 students passed in both subjects, total candidates = (100/55)✕ 495 = 900