The cost prices of two articles P and Q

Question

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

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KanishkM · Answer

Is the answer E ?

Can you please provide the official answer

jackfr2 · Answer

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

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KanishkM · Answer

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.

Giving the answer as E

jackfr2 · Answer

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

btw the correct answer is not 25:14

KanishkM · Answer

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

gvij2017 · Answer

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

E is answer.

jackfr2 · Answer

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

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KanishkM · Answer

Try solving the equation once again(posted by gvij), it is coming as 21/10 only

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bumpbot · Answer

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The cost prices of two articles P and Q

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