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The price of a clock was increased first by a% and then by b% to make

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The price of a clock was increased first by a% and then by b% to make [#permalink] New post   30 Mar 2023, 09:45
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The price of a clock was increased first by a% and then by b% to make it same as the price of another clock. The same change could have been brought by just increasing the price of the clock by c%

Quantity A
Quantity B
a+b
c



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


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Re: The price of a clock was increased first by a% and then by b% to make [#permalink] New post   01 May 2023, 12:58
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Two successive increase of ๐‘Ž% and ๐‘% is overall equal to the net percentage change of (๐‘Ž + ๐‘ +๐‘Ž๐‘/100) % = ๐‘%

i.e. ๐‘Ž + ๐‘ +๐‘Ž๐‘/100= ๐‘

Since a and b are positive, so ๐‘Ž๐‘/100> 0.
As we are adding some positive value ๐‘Ž๐‘/100 to a and b to get c, therefore ๐‘Ž + ๐‘ < ๐‘

Hence, Quantity B is more than Quantity A.
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Re: The price of a clock was increased first by a% and then by b% to make [#permalink] New post   19 May 2024, 19:07
What if both increments were 0% and prices were same from the starting point? it would be D then?
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Re: The price of a clock was increased first by a% and then by b% to make [#permalink] New post   19 May 2024, 22:48
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Yes. on one hand.

On the hand hand, the problem would make no sense with zero increment.

In this kind of problem where the numbers have even an infinite tiny shift the answer is never D
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The price of a clock was increased first by a% and then by b% to make [#permalink] New post   18 Jul 2024, 01:37
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Good Medium level question :)

Assuming Initial cost of clock to be x =1

we have Increase so (1+a/100)+ (1+b/100)= (1+c/100)

According to the question then remaining is simplification

we have a+b=c-100 so, c>a+b.
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The price of a clock was increased first by a% and then by b% to make [#permalink]
18 Jul 2024, 01:37
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