**Problem 1:** In what ratio of two varieties of milk costing Rs.16 and Rs.18 per liter respectively mixed, so the mixture cost RS.16.60 per liter?

Solution:

Basic metod:

16——->x——–>16x

18——->y———>18y

16x+18y = 16.60(x+y)

16x+16y = 16.60x+16.60y

0.60x = 1.40y

Shortcut:

**Problem 2:** The average weight of 30 students in a class is 45 kg. The average weight of girls is 37 kg and that of the boy is 49 kg. Find the number of boys in the class?

Solution:

Basic method:

Boys =x

Girls = (30-x)

x*49 + (30-x)*37 = 30*45

Solving this equation is time taking process.

Shortcut:

2+1=3

3——->30

1———>?

2———->?2*10=20 BOYS

**Problem 3:** A shopkeeper sold 40kg of goods partly at 7% profit and rest at 5% loss, suffering 2% loss on the whole transactions. What is the quantity sold at profit?

Solution:

CP = 100

1+3=4

4——–>40

1———>? KG sold for profit

3———->?3*10 = 30