Question

ਇੱਕ ਪ੍ਰਾਕਿਰਤਿਕ ਸੰਖਿਆ ਵਿੱਚ 12 ਜੋੜਨ 'ਤੇ, ਇਸ ਦਾ ਮੁੱਲ ਇਸ ਦੇ ਉਲਟਕ੍ਰਮ ਦਾ 160 ਗੁਣਾ ਹੋ ਜਾਂਦਾ ਹੈ। ਸੰਖਿਆ ਪਤਾ ਕਰੋ। A natural number, when increased by 12, equals to 160 times of its reciprocal. Find the number. एक प्राकृतिक संख्या में 12 जोड़ने पर इस का मूल्य इसके व्युत्क्रम का 160 गुना हो जाता है। संख्या पता करें। 
(A) 3

(B) 8

(C) 4

(D) 7


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Answer 1

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A situation is given, where when a natural number when increased by 12 equals to 160 times of its reciprocal.

Let, the natural number be x. Then, the reciprocal of the number is 1/x. ATQ,

• Natural no. increased by 12 = x + 12
• 160 times of its reciprocal = 160/x

⇛ x + 12 = 160/x

Cross multiplying,

⇛ x(x + 12) = 160

⇛ x² + 12x = 160

⇛ x² + 12x - 160 = 0

Factorising the above by middle term factorisation,

⇛ x² + 20x - 8x - 160 = 0

⇛ x(x + 20) - 8(x + 20) = 0

⇛ (x + 20)(x - 8) = 0

Then, x = -20 and 8

As it is a natural number, it can't be a negative number i.e. -20.

$\therefore$ So, the number is 8

And we are done !!

Answer 2

Answer:

GIVEN

when a natural number when increased by 12 equals to 160 times of its reciprocal.

TO FIND

Number

SOLUTION

Let's consider the number to be x

• Natural number increased by 12 = x + 12
• 160 multiple by reciprocal = 160/x

We know that

x+12 = 160/x

We have to do cross multiplication

x (x + 12)

x² +12x = 160

x² + 12x = 160

Factorization by middle term

x²+ 20x - 8x - 160 = 0

x(x + 20) - 8(x + 20) = 0

It is equal to (x + 20) (x- 8) = 0

Value of x is equal to 20 or -8

So it is a whole number then it can't be -20

The Answer is 8

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