a man purchased some eggs at 3 for 5 and sold them at 5 for 12.thus he gained 143 in all.the number of eggs he bought is.
Answers
he brought 75 number of eggs
He buys 3 eggs for Rs 5.
Therefore, the cost of one egg = 5/3 Rs.
If he buys n eggs, his total cost is thus 5n/3 Rs.
He sells 5 eggs for Rs 12.
Therefore, the sell price of one egg = 12/5 Rs.
If he sells m eggs, his total takings are thus 12m/5 Rs.
Hence, his net gain = (12m/5 - 5n/3) Rs.
At which point, I have a problem with this Q., since we are not explicitly told that he sells ALL of the eggs that he originally bought. In other words we do not know if n = m. But it seems reasonable to assume that he did. In other words, that n = m.*
On the basis of that assumption, I will now proceed . . .
Net gain = 12n/5 - 5n/3, which, we are told = 143 Rs.
Therefore: 12n/5 - 5n/3 = 143,
i.e.: 11n/15 = 143,
so: n = 195.
► So he bought 195 eggs (assuming that he sold every egg that he bought. i.e., none were stolen; none were taken home; none were dropped and broken and that none were eaten by the seller!).
* Note. You can call me pedantic if you like, but as an amateur mathematician and retired engineer, I have long recognised that it is dangerous to assume anything in a mathematics question!
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