Final answer:
Bipan had 1600 rupees in the beginning.
Step-by-step explanation:
To find out how much money Bipan had in the beginning, we need to calculate the total amount of money he gave to his sister and mother.
Let's assume Bipan had x amount of money initially. He spent 3/4 part of his money for his birthday, so he spent 3/4 * x = 3x/4 on his birthday. He then gave his sister 1/5 part of the remaining money, so he gave 1/5 * (x - 3x/4) = x/20 to his sister. Finally, he gave the rest of the money, which is 120 rupees, to his mother.
Therefore, the equation becomes x - 3x/4 - x/20 = 120. Solving this equation, we find that x = 1600 rupees. So, Bipan had 1600 rupees in the beginning.