- If z varies jointly as x an the square root of y, and if z = 6 when x = 3 and y = 16, find z when x = 7 and y = 4.
Zα jointly as x and √y
Z = 6; x = 3 and y = 16
Z = k x√y
6 = k. 3 x √16 = k. 3 x4 = 12 k
6 = 12 k
k = 6/12 = 1/2
When x = 7 and y = 4 then, Z = k x√y
Z = 1/2 x 7x √4 = 7x2/2 = 7
- The power p, watts, of an electrical circuit varies jointly as the resistance R and the square of the current I. for a 240- watt refrigerator that draws a current of 2 amperes, the resistance is 60 ohms. What is the resistance is – watt microwave over that draws a current of 5 amperes?
According to the given data Pα RI2
P = KRI2
KRI2 = P
K = P/RI2 = 240/60×22 = 240/60×4 = 1
Thus K = 1
When P = 600W and I = 5amps , then R =?
KRI2 = P
K = P/RI2 = 600/1x(5)2 = 600/25 = 24ohms
- The work W done in charging a capacitor varies jointly as the charge q and the voltage V. find the equation of joint variation. If a capacitor with a charge of 0.004 coulomb and a voltage of 100 volts performs 0.20 joule of work, find the constant of proportionally.
W α Qv
W = kQv
W = kx0.004 x100
0.20 = kx0.004 x100
k = 0.20/0.004 x100 = 0.2/0.004 = 0.2/0.4 = 1/2 = 0/5
- The surface area of a cylinder varies jointly as the radius, and the sum of the radius and the height. A cylinder with height 8 cm. and radius 4 cm. has a surface area of 96 πcm². Find the surface area of a cylinder with radius 3 cm and height 10 cm.
A α r(r+h)
A = kr(r+h)
96π = 4k(12)
k = 96 π/4×12
k = 2 π
A = 2 πx3(3+10) = 6 πx13 = 78 πcm2
- The number of hours needed to assemble computers varieties directly as the number of computers and inversely as the number of workers. If 4 workers can assemble 12 computers in 9 hours, how many workers are needed to assemble 48 computers in 8 hours?
Hrs α number of computer α 1/no. of workers
hours no. of computers no. of works
9 12 4
8 48 x
x = 4x48x9/12×8 = 18workers
- The number of litres of water g in a circular tank varies jointly with the square of the radius r2, and the depth d. if g = 3016 when r = 4 and d =2 , find the number of litres in the tank when r = 3 and d= 1.5.
According to the given data g α r2d
Kr2d = g
K = g/R2d = 3016/42x2 = 377/4
When r=3 and d = 15 then g =?
G = Kr2d = 377/4 x (3)2x1.5 = 5089.5/4 = 1272.375litre
- If 36 men can build a wall of 140 m long in 21 days, how many men are required to build a similar wall of length 50 m in 18 days?
Men Length days
36 140m 21
x 50m 18
x= 36x50x21/140×18 = 15men
- If the total wages of 15 labourers for 6 days is rs. 8,100, find the wages of 21 labourers for 5 days.
Labours days rs./wages
15 6 8100
21 5 x
x = 8100x5x21/6×15 = 9450 Rs.
- Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it take to fill the cistern if both of them are opened together?
Tap A takes 8 hours to fill the cistern
Part of cistern filled in 1 hour = 1/8
Tap B empties the cistern in 12 hours
Part of cistern emptied in 1hr = 1/12
Part of cistern filled when both the taps open = 1/8 + 1/12 = 3-2/24 = 1/24
Time taken to fill the cistern when both taps open = 24hours