Hello there ! Magic Maths By OPM @ MalviyaOP OP , welcomes you .
This is a challenging question, please read it carefully.
Mr. Nelson bought some pens and bags. The price of each pen was $ 3.90 while the price for each bag was $ 19.90. For every 4 bags bought, he was given 1 such pen for free . After receiving the free pens, the number of pens was 2/5 of the number of bags. Mr. Nelson paid a total of $ 4097. How much more did he pay for the bags than the pens ?
Here the important point to note is that all pens were not free. Some pens were received free of cost and some pens were bought.
Assume the number of bags bought = B
Number of all pens = 2/5 X B
Since for every 4 bags bought 1 pen was given for free, the number of free pens = B/4
and the number of Paid pens = ( 2/5 B — B / 4 ) = 3B / 20.
We can now write the equation for the amount of money paid for the price of bags and pens bought as below:
Price of bags + Price of Paid pens = $ 4097
$ 19.90 X B + $ 3. 90 X 3 B / 20 = $ 4097
$ 2 0 . 485 B = $ 4097
Therefore, B = 4097 / 20 . 485 = 200
200 Bags were bought . We now knot that the number of paid pens = 3 B / 20 = 3x 200 / 20
= 30.
The money paid for bags = 200 X $ 19.90 = $ 3980.
Money paid for pens = 30 X $ 3.90 = $ 117.
Hence, More money paid for bags = $ ( 3980 - 117 ) = $ 3863 . —— Answer.
How MuCh More Was Paid For The Bags Than The Pens ?
How Many Pens Were Given For Free Of Cost ?
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