Percentage And Its Applications | Quantitative Techniques for CLAT

‘Per cent’ means ‘out of one hundred’. Symbol % is used to denote per cent

Some examples to convert a per cent into a fraction, ratio or decimal and vice versa.

1.
(i) 50% = 0.50

(ii) 7% = 0.07

(iii) 90% =  = 0.90

(iv) 1% = 0.01 

2.
(i) 10% of 100 = 10

(ii) 20% of 500 = 100

(iii) 30% of 1000 = 300

3. 
(i) 5 out of 25 = 20%

(ii) Re 1 out of Rs 25 = 4%

(iii) 10 out of 50 = 20%

Example 1.

(a) If 25% of X= 30. find X

Sol. 25% of X is    and it is equal to 30

(b) If 24% of X is 48, then find X

Sol. 24% of X is 48

Example 2: Vijay deposits Rs 45 per month in the bank. If this amount is 15% of his monthly income, find his monthly income.

Solution: Let his monthly income be Rs X

As per the given statement 15% of X is 45

 or x =  = 300 RS 

Example 3: Gunpowder contains 75% nitre and 10% sulphur. The rest of the material is charcoal. Find the amount of each of the contents in 9 kg of gunpowder.

Solution: Weight of gunpowder = 9 kg

Contents are – nitre = 75%, Sulphur = 10% charcoal = 100-75-10 = 15%

Nitre in 9 kg =  = 6.75 kg

Sulphur in 9 kg =   = 0.90 kg

Charcoal in 9 kg = = 1.35 kg

Example 4: Ankits salary is 25% more than that of Anil. What percent is Anil’s salary less than Ankits?

Solution: Let Anil’s salary be Rs 100

Then Ankit gets 25% more than Anil = 125

If Ankit’s salary is Rs 125 Anil’s = 100

If Ankit’s salary is Rs 100 then Anil’s =

So, Anils salary is Rs 80 when Ankit’s is Rs 100

So, Anil salary is 20% less than Ankit

Example 5: Raman loses 20% of his money. After spending 25% of the remaining, he has Rs 480. How much did he originally had?

Solution: Suppose Raman had Rs 100 in the beginning. He lost 20% i.e. Rs. 20

Remainder = Rs 100 – Rs 20 = Rs 80

Out of Rs 80 he spent 25%, which is equal to

Remainder = Rs 80 – Rs 20 = Rs 60

If remainder is Rs 60, he originally had = Rs 100

If remainder is Rs1, he originally had =

If remainder is Rs 480 he originally had =

Example 6: The price of a shirt in Dec 1997 was Rs 250. In Jan. 1998 it was increased by 10% and in Oct 1998 it was reduced by 10%. What in the new price of the shirt.

Solution: Price in Dec 1997 = Rs 250 

Price in Jan 1998 =

Price in Oct 1998 = 275 x  = Rs 247.50