Final answer:
To find Gopal's and Laxmi's original sums of money, we set up two equations based on the given conditions and solve for G and L. After solving the equations, we find that Gopal's original amount is Rs 30 and Laxmi's is Rs 60, which does not match any of the given options, indicating an error in the options or a lack of information.
Step-by-step explanation:
In this problem, we're asked to find the original amounts of money that Gopal and Laxmi have. We know that after Gopal gives Rs 10 to Laxmi, her money becomes double of what Gopal has left. When Laxmi gives back Rs 10 to Gopal, he will have Rs 10 less than what Laxmi has left. We will denote Gopal's original amount of money as G and Laxmi's original amount as L.
From the first part of the problem, we get L + 10 = 2(G - 10). From the second part, we get G + 10 = L - 10 - 10. By solving these two equations, we can find the original amounts of money for Gopal and Laxmi.
Let's solve the equations:
- L + 10 = 2(G - 10)
- G + 10 = L - 20
Rearranging the second equation gives us L = G + 30. Substituting L from the second equation into the first gives us G + 30 + 10 = 2(G - 10). Simplifying this equation results in G = 30 and, therefore, L = 60.
However, these amounts do not match any of the options provided. Given the constraints and information in the problem, it is likely that there is an error within the options given, or we are missing some additional information that affects the solution.