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# The cost prices of two articles P and Q

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Intern
Joined: 13 Aug 2018
Posts: 10
The cost prices of two articles P and Q  [#permalink]

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Updated on: 17 Oct 2018, 11:10
00:00

Difficulty:

35% (medium)

Question Stats:

92% (01:59) correct 8% (07:23) wrong based on 12 sessions

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The cost prices of two articles , P and Q, are in the ratio 5:7 and their selling prices, in the ratio 2:5 respectively. If the losses made on both the products are the same, what is the ratio between the cost price and the selling price of Q ?
(A) 5:4
(B) 7:3
(C) 8:3
(D) 15:4
(E) none of the above

Posted from my mobile device

Originally posted by jackfr2 on 17 Oct 2018, 10:56.
Last edited by jackfr2 on 17 Oct 2018, 11:10, edited 1 time in total.
Director
Joined: 09 Mar 2018
Posts: 958
Location: India
Re: The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 11:05

_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 13 Aug 2018
Posts: 10
Re: The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 11:11
KanishkM wrote:

sorry I edited the question as none of the answers were correct in the original version

Posted from my mobile device
Director
Joined: 09 Mar 2018
Posts: 958
Location: India
Re: The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 11:33
jackfr2 wrote:
KanishkM wrote:

sorry I edited the question as none of the answers were correct in the original version

Posted from my mobile device

Thank you for the quick turn around.

I followed this approach.

I initially thought of plugging in some values, but was unable to make progress.

P and Q have cost price in the ratio 5:7 and selling price in the ratio 2:5

So if their losses are equal, this means that the percentage change will be equal and negative(loss)

$$\frac{(Selling price(P) - cost price(P))}{cost price(P)}$$ = $$\frac{(Selling price(Q) - cost price(Q))}{cost price(Q)}$$

$$\frac{Selling price(P)}{cost price(P)}$$ = $$\frac{Selling price(Q)}{cost price(Q)}$$

$$\frac{cost price(Q)}{Selling price(Q)}$$ = $$\frac{25}{14}$$ $$\frac{cost price(P)}{Selling price(P)}$$

Since they are ratio we can write the RHS like that.

_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 13 Aug 2018
Posts: 10
The cost prices of two articles P and Q  [#permalink]

### Show Tags

17 Oct 2018, 11:36
KanishkM wrote:
jackfr2 wrote:
KanishkM wrote:

sorry I edited the question as none of the answers were correct in the original version

Posted from my mobile device

Thank you for the quick turn around.

I followed this approach.

I initially thought of plugging in some values, but was unable to make progress.

P and Q have cost price in the ratio 5:7 and selling price in the ratio 2:5

So if their losses are equal, this means that the percentage change will be equal and negative(loss)

$$\frac{(Selling price(P) - cost price(P))}{cost price(P)}$$ = $$\frac{(Selling price(Q) - cost price(Q))}{cost price(Q)}$$

$$\frac{Selling price(P)}{cost price(P)}$$ = $$\frac{Selling price(Q)}{cost price(Q)}$$

$$\frac{cost price(Q)}{Selling price(Q)}$$ = $$\frac{25}{14}$$ $$\frac{cost price(P)}{Selling price(P)}$$

Since they are ratio we can write the RHS like that.

can you solve the question with any approach to get a definitive answer ? I found a way to get an answer but it looked weird , that's why I posted here to see if someone solves it with a different approach

btw the correct answer is not 25:14
Director
Joined: 09 Mar 2018
Posts: 958
Location: India
Re: The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 11:46
Quote:
can you solve the question with any approach to get a definitive answer ? I found a way to get an answer but it looked weird , that's why I posted here to see if someone solves it with a different approach

btw the correct answer is not 25:14

Thank you for the reply. Will try solving it again.
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Senior Manager
Joined: 08 Aug 2017
Posts: 325
The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 17:14
C1 and S1 buy and selling price of P respectively.
C2 and S2 buy and selling price of Q respectively.

C1-S1 = C2- S2
C1-C2 = S1 -S2
C2(C1/C2-1) = S2( S1/S2-1)
Put the value of C1/C2 = 5/7 and S1/S2 = 2/5
Now calculate C2/S2 = 21/15

Intern
Joined: 13 Aug 2018
Posts: 10
Re: The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 19:58
gvij2017 wrote:
C1 and S1 buy and selling price of P respectively.
C2 and S2 buy and selling price of Q respectively.

C1-S1 = C2- S2
C1-C2 = S1 -S2
C2(C1/C2-1) = S2( S1/S2-1)
Put the value of C1/C2 = 5/7 and S1/S2 = 2/5
Now calculate C2/S2 = 21/15

the answer given is 21:10 , so I'm now more confused as ever

Posted from my mobile device
Director
Joined: 09 Mar 2018
Posts: 958
Location: India
Re: The cost prices of two articles P and Q  [#permalink]

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17 Oct 2018, 20:07
Try solving the equation once again(posted by gvij), it is coming as 21/10 only

Posted from my mobile device
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Re: The cost prices of two articles P and Q   [#permalink] 17 Oct 2018, 20:07
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