Clarke was walking on the street, one boy requested her to donate for COVID patients welfare fund. She gave him a Bond note more than half the money she had. She walked a few more steps. Then came a girl who requested her to donate for poor people's fund for which she gave 2 Bond notes more than half the money she had then.
After that, again a boy approached her for an orphanage fund. She gave 3 Bond notes more than half of what she had. At last she had just 1 Bond note remaining in her hand.
How much amount did Clarke have in her pocket when she started ?
Let X be the Bond Notes she initially had.
She gave for the COVID fund one Bond Note more than half of what she had.
i.e.,[1 +(X/2)].
Remaining money = X-(1+X/2) = [(X/2) - 1.
she gave for poor people's, Bond Note 2 more than half what she remained 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 she gave 3 Bond Notes more than half of what she 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 she had one Bond Note remaining so (X-34)/8 = 1
So,
X-34 = 8
X = 8+34 = 42
Hence, Clarke had 42 BondNotes initially in her pocket.
