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

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answer is B.

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Detailed Solution

Given,
The number when decreased by 20 gives the reciprocal of the number.
Assume the whole number as x and form an equation with given data.

⇒ x − 20 = 69 × 1 x ⇒ x (x − 20) = 69 ⇒ x 2 − 20 x = 69 ⇒ x 2 − 20 x − 69 = 0

Solve the equation using the quadratic formula to find x.

x = − (− 20) ± (− 20) 2 − 4 × 1 × (− 69) 2 × 1 ⇒ x = 20 ± 202 + (4 × 69) 2 ⇒ x = 20 ± 400 + 276 2

⇒ x = 20 ± 676 2

⇒ x = 20 ± 26 2

⇒ x = 2 (10 ± 13) 2

⇒

x = 10 ± 13

The number x can be

10 + 13

10 − 13

.
That is, x can be 23 or -3.
Since -3 is not a whole number, x = 23 is the only solution.
So, the value of the required whole number is 23 and the correct option is 2.

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