A distributor sells TVs at 20% profit per piece. He introduced a new scheme that buyer can buy TVs in bulk and will get (n / 10)% off in the total purchase amount (Where n is the number of pieces in the bulk order). In March he sold 100 TVs in one bulk order and the others were single piece order. If he got an overall profit of 10% in March, how many single piece orders were there in March?
A distributor sells TVs at 20% profit per piece. He introduced a new scheme that buyer can buy TVs in bulk and will get (n / 10)% off in the total purchase amount (Where n is the number of pieces in the bulk order). In March he sold 100 TVs in one bulk order and the others were single piece order. If he got an overall profit of 10% in March, how many single piece orders were there in March? Correct Answer 20
Calculation:
The cost price of TV = P
Selling price of TV = (120 / 100) × P = 1.2P
For bulk order of 100, 10% off will be there (n = 100)
Total purchase amount for the bulk order = 100 × (1.2P) × (90 / 100) = 108P
If m is the number of single piece order, total purchase amount = (1.2P) × m = 1.2Pm
Total cost = (100 + m) × P
10% profit from all sales combined.
⇒ (108P + 1.2Pm) / (100 + m)P = 110/100
⇒ (108 + 1.2m) / (100 + m) = 11/10
⇒ 1080 + 12m = 1100 + 11m
m = 20
Important Points
Selling Price = (1 + (x/100)) × cost price where x = profit from one unit (in percentage)
