Find the max no of items he bought.

[Meerak869]

Ramesh went to a wholesale ready made kids store with some money. He could buy 24 hankies, 30 napkins and 40 pairs socks. He retained one-third of money for his travelling expenses. He bought more napkins than hankies which is in turn more than a pair of socks. Find the max no of items he bought.
(a)8 (b)6 (c)4 (d)12 (c)none of these

[RonPurewal]

per the forum rules, please cite the original source of this problem.
(original authorship, please-- no forums or other secondhand sources.)

thank you.

[RonPurewal]

also--
when you post the citation, please ask at least one specific question about this problem.

what do you already understand?
what don't you understand?
what have you tried?
etc.

thanks.

[Meerak869]

source: time institute material

my soln

let us assume the amount he has is A.
A=24H+30N+40S
he retained A/3
so 2A/3=xH+yN+zS
where y>x>z
find max of (x+y+z)?

2A=3xH+3yN+3zS
i got x=16 y=20 z=26.66
as y>x>z
i tried consecutive natural numbers and got 6,9,12,15 out of which 6 and 12 match with the given choices.

is this correct. how can i arrive at proper value. whats the logic behind this.

[RonPurewal]

hmm. well, i've never heard of that source. but, if this problem is any indication, you should be very, very suspicious of this source from now on.

this problem can't be solved, since the words in the problem statement don't even make sense.
e.g.,

"He bought more napkins than hankies which is in turn more than a pair of socks"
... huh?
ok, the red part makes sense. but... the blue part? now we're making some sort of comparison to a single pair of socks (on what basis i don't even know, maybe price)?

[RonPurewal]

also, even if we ignore that part, the rest of the problem is so trivial that something must be wrong with it.

specifically, all of the choices (except E) are ≤ 12.
but, 12 is only half the number of hankies, and it's an even smaller fraction of each of the other two numbers.

so, 12 is half (or less) than the number of each individual item that ramesh can buy.

in other words, even if ramesh bought 12 of each item, he would still be spending less than half the money that he brought.
but, according to the words, ramesh spends 2/3 of his money! so clearly he is buying WAY more than 12 things.

i'm sure that the problem writers intended to ask something else. but, whatever they intended isn't what the words actually say.

again, i would recommend against using this source from now on.