Question
Akash has a few pencils with him. By distributing it
equally to the children he is left with 3 pencils. If there were 2 students lesser, he would have been left with only 1 pencil on distributing it equally by giving 2 additional pencils to each child. Had there been 4 children less than the original number, each child would have got 5 additional pencils and Akash would have been left with 3 pencils. How many pencils does Akash have?Solution
Let original number of children = x, and pencils per child = y
We have xy + 3 = (x-2)(y+2) + 1
or xy + 3 = xy + 2x - 2y - 4 + 1
or x - y = 3 or x = y + 3
Next we have:
xy + 3 = (x-4)(y+5) + 3
xy + 3 = xy +5x - 4y -20 + 3
5x - 4y = 20
Since x = y + 3, 5y + 15 - 4y = y + 15 = 20
y = 5, x = 8
Total pencils = xy + 3 = 43
42, 54, 78, 114, 168, 222
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