Procedure

Sometimes we are given two quantities and we want to find what per cent of one quantity is of the other quantity. In other words, we want to find how many hundredths of one quantity should be taken so that it is equal to the second quantity. In such type of problems, we proceed as discussed below:

Let a and b be two numbers and we want to know: what per cent of a is b ?

Let x% of a be equal to b. Then,

                    \(\frac{ x}{ 100}\)    x a = b

                    => x = b x \(\frac{ 100}{ a }\)
                    => x = \(\frac{ b}{ a}\) x lOO

            Thus, b is (\(\frac{ b}{ a }\) x 100)% of a.

Illustrative Examples:

Example 1: What per cent of 25 kg is 3.5 kg?

Solution. We have,

            Required per cent = ( \(\frac{ 3.5 kg}{ 25 kg}\) x 100) = \(\frac{ 3.5 * 100}{ 25}\)

= \(\frac{ 35 * 100}{ 250}\)

=\(\frac{ 35 * 2}{ 5}\)

= 7x 2

= 14
           

Hence, 3.5 kg is 14% of 25 kg.

Alternative Solution-
          

Let x% of 25 kg be 3.5 kg. Then,
           

x% of 25kg = 3.5kg
          

=> \(\frac{ x}{ 100}\) x 25 = 3.5
           

=> x = \(\frac{ 3.5 * 100}{ 25}\)     [Multiplying both sides by \(\frac{ 100}{ 25}\) ]
          

=> x = \(\frac{ 35 * 100}{ 250}\) = \(\frac{ 35 * 2}{ 5}\) = 7 x 2 = 14.

Example 2: Express 75 paise as a per cent of Rs 5.

Solution. We have, Rs 5 = 500 paise.

Let x% of Rs 5 be 75 paise. Then,

x% of Rs 5 = 75 paise

=> x% of 500 paise = 75 paise

=> \(\frac{ x}{ 100}\) x 500 = 75

=> x = \(\frac{ 75 * 100}{ 500}\)

=> x = 15.

Hence, 15% of Rs 5 is 75 paise.

Alternative Solution-  The required per cent = ( \(\frac{ 75}{ 500}\) x 100) % = 15%

Example 3 : Find 10% more than Rs 90.
Solution. We have,

10% of Rs 90 = Rs ( \(\frac{ 10 }{ 100}\) x 90 ) = Rs 9
       

Therefore, 10% more than Rs 90 = Rs 90 + Rs 9 = Rs 99

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