Question

A jewellery shop owner conducts his business in the
following manner. Every once in a while he raises
his prices by a certain percentage and a while later
he reduces his prices by the same percentage. After
one such updown cycle of increasing and then
decreasing his price by x%, the price of a jewel
decreases by 100. In the next cycle, he increases
and then decreases his price by (x/2)% and then
sells the jewel for 2376. What is the initial price of
the jewel (in )?
(B) 2475
(D) 2575
(A) 2450
(C) 2500​

Answer 1

Answer:

A

2756.25

⇒ Let the original price be P and X%=a

⇒ P−P×(1+a)(1−a)=441

⇒ P×a

2

=441 ---- ( 1 )

⇒ Again, P×[(1+a)(1−a)]

2

=1944.81

⇒ P×(1−a

2

)

2

=1944.81 ----- ( 2 )

Dividing ( 2 ) by ( 1 ). we get,

⇒

P×(a

2

)

P×(1−a

2

)

2

=

441

1944.81

⇒

a

2

(1−a

2

)

2

=4.41

⇒

a

1−a

2

=2.1 [Taking square root on both sides]

∴ a=

5

2

⇒ P×(

5

2

)

2

=441 [Substituting value in ( 1 )]

⇒ P=

4

441×25

=Rs.2756.25