A sold a mobile phone to B at a gain of 25% and B sold it to C at a loss of 10%. If C paid ₹5,625 for it, how much did A pay (in ₹) for the phone?

The correct answer is 5,000.

Let us break down the transaction step-by-step to find the price paid by A.

Let the cost price of the mobile phone for A be x rupees.

Step 1: Transaction from A to B
A sells the mobile phone to B at a gain of 25%.
Therefore, the cost price for B (which is the selling price for A) is:
Cost Price for B = x + 25% of x
$\mathrm{Cost\; Price\; for\; B}=x\times (1+0.25)=1.25x$

Step 2: Transaction from B to C
B sells the mobile phone to C at a loss of 10%.
Therefore, the price C pays is 10% less than B's cost price:
Price paid by C = Cost Price for B - 10% of Cost Price for B
$\mathrm{Price\; paid\; by\; C}=1.25x\times (1-0.10)=1.25x\times 0.9$

Step 3: Solve for x
We are given that C paid ₹5,625 for the mobile phone.
So, we can set up the equation:
$1.25x\times 0.9=5625$
Let's simplify the multiplication:
$1.125x=5625$
Now, divide both sides by 1.125 to solve for x:
$x=\frac{5625}{1.125}$
$x=5000$

Thus, A paid ₹5,000 for the phone.