Question

17. The price of an item is increased by p% and later it is decreased by
p%. If present price is Rs. 1, then what was the original price of the
item?​

Answer 1

Answer:

Required price of item should be Rs 10000 / ( 10000 - p^2 ).

Step-by-step explanation:

Let,

Original price of that item be Rs a.

When price is increased by p% :

= > Original price + p% of original price

= > Rs a + p% x Rs a

= > Rs a ( 1 + p% )

= > Rs a ( 1 + p / 100 )

After that : Price is decreased by p% and remaining price is 1 rupee.

= > Rs a( 1 + p / 100 ) - p% of Rs a( 1 + p / 100 ) = Rs 1

= > Rs a( 1 + p / 100 ) - p% x Rs a( 1 + p / 100 ) = Rs 1

= > a( 1 + p / 100 ){ 1 - p% } = 1

= > a( 1 + p / 100 )( 1 - p / 100 ) = 1

From the properties of expansion :

• ( a + b )( a - b ) = a^2 - b^2

= > a [ ( 1 )^2 - ( p / 100 )^2 ] = 1

= > a [ 1 - p^2 / 10000 ] = 1

= > a[ ( 10000 - p^2 ) / 10000 ] = 1

= > a = ( 10000 ) / ( 10000 - p^2 )

= > Rs a = Rs 10000 / ( 10000 - p^2 )

Hence the required price of item should be Rs 10000 / ( 10000 - p^2 ).