Mr. Sinha received a certain amount of money by winning a lottery contest. He purchased a new vehicle with 40 percent of the money received. He then gave 20 percent of the remaining amount to each of his two sons for investing in their business. Thereafter, Mr. Sinha spent half of the remaining amount for renovation of his house. One-fourth of the remaining amount was then used for purchasing a LCD TV and the remaining amount - Rs. 1,35,000/- was deposited in a bank. What was the amount of his cash prize?

He purchased a new vehicle with 40 percent of the money received. He then gave 20 percent of the remaining amount to each of his two sons for investing in their business. Thereafter, Mr. Sinha spent half of the remaining amount for renovation of his house. One-fourth of the remaining amount was then used for purchasing a LCD TV and the remaining amount - Rs. 1,35,000/- was deposited in a bank. What was the amount of his cash prize?

Let '100x' be the amount won by Mr. Sinha in the lottery contest. 

The amount left with him after purchasing the new vehicle = 0.60*100x = 60x.

The amount left with him after distributing his two sons for investing in their business = (1-2*0.20)*60x = 36x.

The amount left with him after renovating his house = 0.50*36x = 18x.

The amount left with him after purchasing the LCD TV = 0.75*18x = 13.5x.

It is given that, 13.5x = 135000

Therefore, 100x = 10,00,000. Hence, option A is the correct answer.