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Director  V
Joined: 18 Feb 2019
Posts: 581
Location: India
GMAT 1: 460 Q42 V13 GPA: 3.6
An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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11 00:00

Difficulty:   55% (hard)

Question Stats: 64% (02:31) correct 36% (02:26) wrong based on 107 sessions

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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 t%. What is its cost price?

A. 100r/(t-s)
B. 100s/(t-r)
C. s/100(t-r)
D. st/100(t-r)
E. (t-r)/100s
Senior Manager  P
Joined: 03 Mar 2017
Posts: 367
Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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1
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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Senior Manager  P
Joined: 03 Mar 2017
Posts: 367
Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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1
Quote:
Let the profit be p .
The CP be denoted by c

From the first case using Profit % formula.

Quote:
Profit%=(Profit*100)/C.P

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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All the Gods, All the Heavens, and All the Hells lie within you.
Intern  B
Joined: 18 Jan 2019
Posts: 28
Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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warrior1991 wrote:
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.

where did you get pr+sr=pt from? can you please explain this? Also is there any general topic that these equations are derived from?
Senior Manager  P
Joined: 03 Mar 2017
Posts: 367
Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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Ish1996 wrote:
warrior1991 wrote:
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.

where did you get pr+sr=pt from? can you please explain this? Also is there any general topic that these equations are derived from?

Read the equation just above the equation you talking about

Sent from my iPhone using GMAT Club Forum mobile app
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All the Gods, All the Heavens, and All the Hells lie within you.
Manager  B
Joined: 03 Sep 2018
Posts: 177
An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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1
1
Above solutions are unnecessarily difficult

P=R-C

r(C)/100=R-C –> R=C(r/100+1)

t(C)/100=R+s-C –> t(C)/100=C(r/100+1)+s-C –> t(C)/100=r(C)/100+s –> C=S/((t-r)/100)=100(S)/(t-r)
Intern  B
Joined: 23 Jun 2019
Posts: 2
Location: United States
Concentration: Economics, Statistics
Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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Essentially we are dealing with three numbers. Suppose we are starting with 20, after r% profit the number becomes 30 and adding 10 the number finally becomes 40. That is 20...30...40
Now r=50 [ increase is 50%]
S= 10
t= 100 [ increase is 100%]
If we substitute these values the correct expression must give the cost, which is 20.
A. 100r/(t-s) =100*50/90 [does not work]
B. 100s/(t-r) =100*10/50 =20 [works!]
C. s/100(t-r) = 10/100*50 [does not work]
D. st/100(t-r) =10*100/100*50 [does not wok]
E. (t-r)/100s = 50/100*10 [Does not work]

Therefore, B is the answer.

Please note that I avoided using 100 as the starting value because often time it cannot eliminate all the incorrect answers. Hope this helps! Re: An item, when sold at a certain price, yields r% profit. Had it been s   [#permalink] 26 Aug 2019, 00:33
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