A man buys 120 toys each at the same cost price. He sells 45% of the toys at 40% profit, one-third of the remaining at 20% profit, and the remaining at a loss which is equal to the cost price of 14 toys. His profit per cent in the entire transaction is:

Let the cost price (CP) of each toy be Rs. 1.
Total CP for 120 toys = Rs. 120.

First part: Sells 45% of the toys

Number of toys=45% of 120=
100
45
​
×120=54
Profit=40% of 54=
100
40
​
×54=Rs. 21.6
Second part: Sells one-third of the remaining toys

Remaining toys=120−54=66
Number of toys=
3
1
​
×66=22
Profit=20% of 22=
100
20
​
×22=Rs. 4.4
Third part: Sells the remaining toys at a loss equal to the CP of 14 toys

Remaining toys=66−22=44
Loss=CP of 14 toys=Rs. 14
Net Profit Calculation:

Total Profit/Loss=Profit
1
​
+Profit
2
​
−Loss
Total Profit=21.6+4.4−14=26−14=Rs. 12
Profit Percentage:

Profit %=(
Total CP
Total Profit
​
)×100
Profit %=(
120
12
​
)×100=10%