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An item, when sold at a certain price, yields r% profit

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Bijesh
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An item, when sold at a certain price, yields r% profit [#permalink] New post   01 Jul 2019, 05:31
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An item, when sold at a certain price, yields r% profit. Had it been sold for $s more, the profit percentage would have been r%. What is its cost price?

A) \(\frac{100r}{(t-s)}\)

B) \(\frac{100s}{(t-r)}\)

C) \(\frac{s}{100(t-r)}\)

D) \(\frac{st}{100(t-r)}\)

E) \(\frac{(t-r)}{100s}\)
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Re: An item, when sold at a certain price, yields r% profit [#permalink] New post   01 Jul 2019, 07:12
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\(r=\frac{(p*100)}{c}\)

\(t=\frac{((p+s)*100)}{c}\)

After manipulation we will end up with

\(c=\frac{100s}{(t-r)}\)

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Bijesh
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Re: An item, when sold at a certain price, yields r% profit [#permalink] New post   01 Jul 2019, 07:13
Thank you
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AlaminMolla
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Re: An item, when sold at a certain price, yields r% profit [#permalink] New post   08 Jul 2019, 16:28
Hi there, can you please elaborate the whole procedure? I am sorry but struggling to catch it.

Thanks.
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Re: An item, when sold at a certain price, yields r% profit [#permalink] New post   15 Jul 2019, 09:58
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Let the profit be p .
The CP be denoted by c

From the first case using Profit % formula.

r=(p*100)/c ---1

After S.P is increased by s$

t=((p+s)*100)/c----2

Therefore from 1 and 2

r/t=p/(p+s)

pr+sr=pt

p(t-r)=sr

Put value of r from e.q-1---

p(t-r)=s(p*100)/c

Both P got cancelled

(t-r)=100s/c

c=100s/(t-r)

IMO B.
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Re: An item, when sold at a certain price, yields r% profit [#permalink] New post   29 Aug 2019, 07:40
Bijesh wrote:
An item, when sold at a certain price, yields r% profit. Had it been sold for $s more, the profit percentage would have been r%. What is its cost price?

A) \(\frac{100r}{(t-s)}\)

B) \(\frac{100s}{(t-r)}\)

C) \(\frac{s}{100(t-r)}\)

D) \(\frac{st}{100(t-r)}\)

E) \(\frac{(t-r)}{100s}\)


I am confused. I think the question is poorly formulated.
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Re: An item, when sold at a certain price, yields r% profit [#permalink] New post   30 Apr 2024, 12:44
The question stem has no mention of the variable t. I think it should be

Bijesh wrote:
Had it been sold for $s more, the profit percentage would have been t%.
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gmatclubot
Re: An item, when sold at a certain price, yields r% profit [#permalink]
30 Apr 2024, 12:44
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