What value should come in the place of question mark (?) in the following question:
\(0.5\overline{27} - 0.3\overline{25} + 0.2\overline{24} = ?\)

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UP Police SI (दरोगा) Official PYP (Held On: 25 Nov 2021 Shift 2)
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  1. 422/990
  2. 412/990
  3. 432/990
  4. 402/990

Answer (Detailed Solution Below)

Option 1 : 422/990
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UP Police SI (दरोगा) Official PYP (Held On: 2 Dec 2021 Shift 1)
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Detailed Solution

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Given:

0.527 - 0.325 + 0.224 = ?

Formula used:

A repeating decimal 0.abc can be written as (abc - a) / 990

A repeating decimal 0.ab can be written as ab / 99

Calculation:

0.527 = (527 - 5) / 990 = 522 / 990

0.325 = (325 - 3) / 990 = 322 / 990

0.224 = (224 - 2) / 990 = 222 / 990

⇒ ? = 522 / 990 - 322 / 990 + 222 / 990

⇒ ? = (522 - 322 + 222) / 990

⇒ ? = (200 + 222) / 990

⇒ ? = 422 / 990 

The correct answer is Option (1).

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