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# An item, when sold at a certain price, yields r% profit. Had it been s

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Director
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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01 Mar 2019, 10:36
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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
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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01 Mar 2019, 20:58
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
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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01 Mar 2019, 20:59
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
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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02 Mar 2019, 01:45
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
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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02 Mar 2019, 02:36
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?

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
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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23 Aug 2019, 01:20
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
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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26 Aug 2019, 00:33
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]

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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