**Application of Rule of Alligation in TSD and Profit/Loss**

Eg: A person covers 800km partly at a speed of 50kmph and partly at a speed of 150kmph, in 10 hours over all. What is the distance covered at the speeds of 150 kmph?

Average speed = 800/10 = 80 kmph

Apply Rule of Alligation

50 kmph .... 150 kmph

... 80 kmph ...

70 : 30 ( 150 - 80 = 70 : 80 - 50 = 30 )

So out of 10 hours, 30 x 10 / 100 = 3 hours in 150 kmph.

So distance covered = 150 kmph x 3 = 450 km.

Eg: Shopkeeper sold 45 kg of goods. If he sells some quantity at a loss of 3% and rest at 17% profit, making 5% profit on the whole, find the quantity sold at profit?

17% ... -3% (Loss)

.... 5% ....

8 : 12

At Profit : At loss = 8 : 12

Quantity sold at profit = 45 x 8/20 = 18 kg