**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.**

Solution:

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 = 7x^{2}/_{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?**

Solution:

According to the given data Pα RI^{2}

P = KRI^{2}

KRI^{2} = P

K = ^{P}/_{RI}^{2} = ^{240}/_{60×2}^{2} = ^{240}/_{60×4} = 1

Thus K = 1

When P = 600W and I = 5amps , then R =?

KRI^{2} = P

K = ^{P}/_{RI}^{2} = ^{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.**

Solution:

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.**

Solution:

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 πcm^{2}

**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?**

Solution:

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.**

Solution:

According to the given data g α r^{2}d

Kr^{2}d = g

K = ^{g}/_{R}^{2}d = ^{3016}/_{4}^{2}_{x2} = ^{377}/_{4}

When r=3 and d = 15 then g =?

G = Kr^{2}d = ^{377}/_{4} x (3)^{2}x1.5 = ^{5089.5}/_{4} = 1272.375litre

- I
**f 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?**

Solution:

Men Length days

36 140m 21

x 50m 18

x= ^{36x50x21}/_{140×18} = 15men

- I
**f the total wages of 15 labourers for 6 days is rs. 8,100, find the wages of 21 labourers for 5 days.**

Solution:

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?**

Solution:

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

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