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Given data:

Sum of Rs = 3.75

Was paid in 25 paise, 10 paise and 5 paise coins.

Let the number of 25 paise coins be X.

And let the number of 5 paise coins be Y.

And it is given that 10 paise coins are 4 times the number of 25 paise coins.

So the number of 10 paise coins = 4 times the number of 25 paise coins.

So the number of 10 paise coins = 4X......... (1)

And it is also that 10 paise coins are twice the number of 5 paise coins.

So the number of 10 paise coins = 2Y............ (2)

Now from equation (1) and (2) we have,

4X = 2Y

Therefore, Y = 2X.

So the number of 5 paise coins are 2X, 10 paise coins are 4X, and 25 paise coins are X.

Now as we know that in one rupee there are 100 paise.

So in 3.75 rupees there are 100 (3.75) = 375 paise.

Now the sum of the product of respective paise with the respective number of coins is equal to the required paise which is paid.

$ \Rightarrow \left( {5 \times 2X} \right) + \left( {10 \times 4X} \right) + \left( {25 \times X} \right) = 375$

$ \Rightarrow 10X + 40X + 25X = 375$

$ \Rightarrow 75X = 375$

$ \Rightarrow X = \dfrac{{375}}{{75}} = 5$