Question

One day when Ram was walking on the street , one biy requested him to donate for cancer patients welfare fund. he gave him a rupee more than half of the money he had. He walked a few more steps. Then came a girl who requested him to donate for poor peoples's fund for which he gave two rupees more than half the money he had then. After that , again a boy approached him for an orphanage fund. He gave three rupees more than half of what he had. At last he had just one rupee remaining in his hand. How much amount did Ram have in his pocket when he started ?

• A. Rs. 72
• B. Rs. 58
• C. Rs. 35
• D. Rs. 42

Answer 1

The correct option is D Rs. 42

Let x be the rupees Ram initially had.
He gave a rupee more than half the money he had for cancer fund.
i.e., he gave Rs 1 + x/2
So the remaining amount = x - (1 + x/2) = x/2- 1
Then he offered 2 rupees more than half the money he had for poor people's fund.
i.e., he gave 2 + 1/2 x(x/2 - 1 = 2 + (x-2)/4 = (6 + x)/4
So, the remaining money = x/2 - 1 - (6 + x)/4 = (x - 10)/4
Again he gave 3 rupees more than half of what he had for orphanage
i.e., he gave 3 + 1/2x (x - 10)/4 = 3 + (x - 10)/8 = (14 + x )/8
mow the remaining money = (x - 10)/ 4 - (14 + x ) / 8 = (2x - x - 20 - 14)/8 = (x - 34)/8
As given , finally he had one rupee remaining so, (x - 34) / 8 = 1
i.e. , x - 34 = 8
x = 8 + 34 = 42
Hence, Ram had Rs. 42 initially in his pocket.