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

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Joined: 18 Feb 2019
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GMAT 1: 490 Q47 V13
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An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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New post 01 Mar 2019, 10:36
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  55% (hard)

Question Stats:

64% (02:54) correct 36% (02:26) wrong based on 36 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
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Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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New post 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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Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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New post 01 Mar 2019, 20:59
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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Joined: 18 Jan 2019
Posts: 9
Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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New post 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?
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Re: An item, when sold at a certain price, yields r% profit. Had it been s  [#permalink]

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New post 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?


Read the equation just above the equation you talking about


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Re: An item, when sold at a certain price, yields r% profit. Had it been s   [#permalink] 02 Mar 2019, 02:36
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