Question

Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

Answer 1

SOLUTION :  

Let the whole number = x

Reciprocal of the number  = 1/x

A.T.Q

(x - 20) = 69 × 1/x

(x - 20) = 69 /x

x - 69/x = 20

(x²  - 69)/x = 20

[By taking LCM]

(x²  - 69) = 20x

x²  - 20x  - 69 = 0

x²  - 23x + 3x - 69 = 0

[By middle term splitting method]

x(x - 23) + 3(x - 23) = 0

(x - 23) (x + 3) = 0

(x - 23)  = 0  or (x + 3) = 0

x = 23  or  x =  -3

since, whole number can't be negative,  x ≠  -3

Therefore, x = 23

Hence, the whole number be 23.

HOPE THIS  ANSWER WILL HELP YOU..

Answer 2

Solution :

Let the required whole number = x

According to the problem given,

x - 20 = 69/x

=> x( x - 20 ) = 69

=> x² - 20x - 69 = 0

=> x² - 23x + 3x - 69 = 0


=> x( x - 23 ) + 3( x - 23 ) = 0

=> ( x - 23 )( x + 3 ) = 0

=> x - 23 = 0 or x + 3 = 0

=> x = 23 or x = -3

But ,x is a whole number ,

x = 23

Therefore ,

Required whole number = 23

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