t shirt company makes polo shirts with expectation that it will earn a profit of 50% by selling each shirt at its marked price.but during delivery to show rooms,17% of shirts were completely solied and hence could not be sold, 18% of shirts were slightly soiled and hence could be sold at 70% of cost price and remaining was sold at marked price.what is % profit in whoile consignment ?

let's assume there are 100 shirts, with a cost of $100 each.

17 are not sold: $0
18 are sold for $70 each: $1260
65 are sold for $150 each: $9750

total income: 11010

profit is thus 1010/10000 = 10.1%

To find the overall profit percentage for the entire consignment, we need to calculate the profit percentage for each category separately: completely soiled shirts, slightly soiled shirts, and the remaining shirts sold at the marked price.

1. Completely soiled shirts:
Since 17% of the shirts were completely soiled and could not be sold, there is no profit or loss associated with them.

2. Slightly soiled shirts:
18% of the shirts were slightly soiled and could be sold at 70% of the cost price. This means they incur a loss of 30% on the cost price.

3. Remaining shirts sold at the marked price:
Since the remaining shirts were sold at the marked price, a profit of 50% is earned on each of these shirts.

Next, we calculate the weightage of each category in terms of the total number of shirts:

- Completely soiled shirts: 17%
- Slightly soiled shirts: 18%
- Remaining shirts sold at marked price: 100% - (17% + 18%) = 65%

Now, let's calculate the overall profit percentage:

Overall profit percentage = (Weightage of completely soiled shirts * profit percentage for completely soiled shirts)
+ (Weightage of slightly soiled shirts * profit percentage for slightly soiled shirts)
+ (Weightage of shirts sold at marked price * profit percentage for shirts sold at marked price)

Overall profit percentage = (17% * 0) + (18% * (-30%)) + (65% * 50%)

Simplifying this equation, we get:

Overall profit percentage = -5.1% + 9% + 32.5%
Overall profit percentage = 36.4%

Therefore, the overall profit percentage for the entire consignment is 36.4%.