on giving 3 pencils free with every 5 pens bought, a shopkeeper makes a profit of 20% and on giving 6 pencils free with every 2 pens bought, he suffers a loss of 25%. find the approx profit percentage made by the shopkeeper when he gives 4 pencils free with every 6 pens bought
Answers
Answer:
18 %
Step-by-step explanation:
Let say Pencil Cost Price = A
Pen Cost Price = B
Pen Selling Price = C
3 pencils free with every 5 pens gives 20% Profit
Cost Price = 3A + 5B
Profit 20% = (20/100)(3A + 5B) = 0.6A + B
Selling Price = 3A + 5B + 0.6A + B = 3.6A + 6B
Selling Price = 5C
5C = 3.6A + 6B Eq1
6 pencils free with every 2 pens
Cost Price = 6A + 2B
Loss 25% = (25/100)(6A + 2B) = 1.5A + 0.5B
Selling Price = 6A + 2B - 1.5A - 0.5B = 4.5A + 1.5B
Selling Price = 2C
2C = 4.5A + 1.5B Eq2
5* eq 1 - 4* eq 2
=> 17C = 24B
=> B = 17C/24
4*eq2 - Eq1
=> 3C = 14.4A
=> A = C/4.8
=> A = 5C/24
4 pencils free with every 6 pens
Cost Price = 4A + 6B = 4(5C/24) + 6(17C/24) = 122C/24 = 61C/12
Selling Price = 6C
Profit = 6C - 61C/12 = 11C/12
Profit % = { (11C/12)/(61C/12) } * 100 = 18 % (approx)