If A varies directly with B and C both , then show that A varies directly with (B-C) .

To dig a well of x dcm deep , one part of the total expenses varies directly with x and other part varies directly with x^2 . If the expenses of digging wells of 100 dcm and 200 dcm depths are rs5000 and rs12000 respectively , calculate the expenses of digging a well of 250 dcm depth.

A variable is the sum of two such quantities one of which varies directly with x and the other varies directly with x^2 . If y =3 when x =1 and y=10 when x=2 , then find the relation between x and y .

To dig a well of x dcm deep, one part of the total expenses varies directly with x and other part varies directly with x^2 . If the expenses of digging well of 100 dcm depths are Rs 5000 and Rs 12000 respectively. Calculate the expenses of digging a well of 250 dcm depth.

y is sum of two variables, one in which varies directly with x and another varies inversely with x. When x= 1 then y = 1 and x = 3 the y = 5. Find the relation between x and y,

Volume of a sphere varies directly with cube of length of its radius and surface area of sphere varies directly with the square of the length of radius. Prove that the square of volume of sphere varies directly with cube of its surface area.

The rms velocity of an ideal gas varies directly with its density as —

x varies directly with y and inversely with z if y y =4 ,z=5, then x=3 . Again ,if y=16 , z=30 , then find the value of x .

y varies directly with square root of x and y =9 when x =9 . Find the value of x when y =6 .

The time of going from one place to another varies directly as the distances and inversely as the speed . Two trains describe distances which are in the ratio of 5:8 and times required are in the ratio of 4:7 . Find the ratio of their speeds .

Group of N cells whose e.m.f. varies directly with the internal resistance, as per the equation E_N = 1.5 r_N are connected as shown in fig .Find the current I in the circuit.