Question

A person gives two successive discount 0f x% on rs.720 and sells it at 259.20. Find the value of x?

Answer 1

Answer:

A person gives two successive discount 0f x% on rs.720 and sells it at 259.20. Find the value of x?

The discount x, is 20%

Step-by-step explanation:

Successive Discount is given by the following formula:

If the first discount is x% and 2nd discount is y% then ,

Total discount = ( x + y - xy / 100 ) %

In this case, both the first and second discount is x, therefore the formula will be:

( x + y - xy / 100 ) %

= ( x + x - x(x)/100)%

= (2x -x²)/100 %

This is the successive discount.

Therefore:   (2x -x²)/100 % of 720 = 259.2

                 ⇒ (2x -x²/100) × 1/100 × 720 = 259.2

                 ⇒ 2x -x²/100 = 259.2 ×100/720

                 ⇒ 2x - x²/100  = 36

                 ⇒ 200x - x² = 3600

                 ⇒ x² - 200x + 3600 = 0

Solve using product sum method:

x² - 200x + 3600 = 0

x² - 180x - 20x + 3600 = 0

x(x -180) - 20( x - 180) =

( x - 180) (x - 20) = 0

Therefore; x -180 = 0 or x - 20 = 0

Therefore  x = 180 or 20

Therefore the discount is either 180% or 20%. If the discount was 180%, it would be a loss, therefore x = 20%

         x = 20%

The other way of getting this successive discount is by going step-by-step and not using the formula:

x/100 × 720 = 7.2x

7.2 is the first discount

Subtract this from 720

720 - 7.2x

Get the next discount

x/100 (720 - 7.2x)

= 7.2x - 0.072x²

7.2x - 0.072x² is the second discount

Therefore: The sum of the two discounts should be equal to the total discount given

7.2x - 0.072x² + 7.2x = 259.2

14.4x - 0.072x² = 259.2

14400x - 72x² = 259200

72x² - 14400x + 259200 = 0

Solve using product sum method, just we did with the equation above:

x = 20%

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