let

x = the number of 25 paisa coins

y = the number of 50 paisa coins

bag contains 25 paisa and 50 paisa coins whose total value =2400

25x + 50y = 2400

the number of 25 paisa coin is 4 times that of 50 paisa coins

x = 4y

by solving the system of equations

25x + 50y = 2400

x = 4y

we find

x = 64

y = 16

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there 64 25-paisa coins and 16 50-paisa coins in the bag.