Question
Rohit was walking on the street, one boy requested him to donate for cancer patients welfare fund. He gave him a rupee more than half the money he had. He walked a few more steps. Then came a girl who requested him to donate for poor people'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?
How much amount did Ram have in his pocket when he started?
Answer: Option C
Let X be the rupees he initially had.
He gave for the cancer fund one rupee more than half of what he had.
i.e.,[1 +(X/2)].
Remaining money = X-(1+X/2) = [(X/2) - 1.
he gave for poor people's, rupee 2 more than half what he remain with,
= [2+{1/2*(X/2-1)}]
= [2+{(X-2)/4}]
= (6+X)/4
Now, 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,
[3+(1/2*((X-10)/4))]
= 3+[(X-10)/8]
= (14+X)/8
now left 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
So,X-34 = 8
X = 8+34 = 42
Hence, Rohit had Rs. 42 initially in his pocket.
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Let X be the rupees he initially had.
He gave for the cancer fund one rupee more than half of what he had.
i.e.,[1 +(X/2)].
Remaining money = X-(1+X/2) = [(X/2) - 1.
he gave for poor people's, rupee 2 more than half what he remain with,
= [2+{1/2*(X/2-1)}]
= [2+{(X-2)/4}]
= (6+X)/4
Now, 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,
[3+(1/2*((X-10)/4))]
= 3+[(X-10)/8]
= (14+X)/8
now left 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
So,X-34 = 8
X = 8+34 = 42
Hence, Rohit had Rs. 42 initially in his pocket.
Was this answer helpful ?
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