Question

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Answer 1

Step-by-step explanation:

Given :-

0.235 bar on 35 + 15.712 bar on 12

To find :-

Express it in p/q form ?

Solution :-

Given that

0.235 bar on 35 + 15.712 bar on 12

On taking 0.235 bar on 35

Let X = 0.235 bar on 35

=> X = 0.2353535... ---------------(1)

Since the periodicity is 2 then we multiply (1) with 100 then

=> 100×X = 0.2353535...×100

=> 100X = 23.53535...-------------(2)

On Subtracting (1) from (2) then

100X = 23.53535...

X = 0.23535...

(-)

________________

99X = 23.3

________________

=> 99X = 23.3

=> 99X = 233/10

=> X = 233/(99×10)

=> X = 233/990

0.235,bar on 35 = 233/990 ----------(3)

and

On taking 15.712 bar on 12

Let X = 15.712 bar on 12

=> X = 15.7121212... ---------------(4)

Since the periodicity is 2 then we multiply (1) with 100 then

=> 100×X = 15.7121212...×100

=> 100X = 1571.21212...-------------(5)

On Subtracting (1) from (2) then

100X = 1571.21212...

X = 15.71212...

(-)

________________

99X = 1555.5

________________

=> 99X = 1555.5

=> 99X = 15555/10

=> X = 15555/(99×10)

=> X = 15555/990

15.712 bar on 12 = 15555/990 ----------(6)

On adding (3) and (6)

=> 0.235 bar on 35 + 15.712 bar on 12

=> (233/990)+(15555/990)

=> (233+15555)/990

=> 15788/990

=> 7894/495

=> 15.947474...

=> 15.9474 bar on 74

Answer:-

0.235 bar on 35 + 15.712 bar on 12 = 15.9474 bar on 74

Used formulae:-

→ If the periodicity is 2 then multiply the given equation with 100

Answer 2

Solution,

Let x = 0.235 bar on 35

=> x = 0.2353535

=> 100 × x = 0.2353535..× 100

=> 100x = 23.53535....

Now subtract

100x = 2353535..

x = 0.2353535

=> 99x = 23.3

=> 99x = 23.3

=> 99x = 233/10

=> x = 233/(99×10)

=> x = 233/990

0.235 bar on 35 = 233/990

The periodicity is 2 when multiply

=> 100 × x = 15.+121212...

=> 100x = 1571.21212....

When subtract

100x = 1571.21212....

x = 15.71212

990x = 1555.5

=> 990x = 15555/10

=>x = 15555 / (99×10)

=> x = 15555/990

= 15.712

15.712 bar on 12 = 15555/990

On Adding

=> 0.235 bar on 35 + 15.712 bar on 12

=> (233/990) + (15555/990)

=> (233/15555)/990

=> 15788/990

=> 7894/495

=> 15.9474 bar on 74

Hence, 0.235 bar on 35 + 15.712 bar on 12 = 15.9474 bar on 74