If N = 0.738738738738… and M = 0.531531531531….., then what is the value of (1/N) + (1/M)?

1. 2448/11100

2. 15651/4838

3. 11100/2419

4. 1897/3162

1. 2448/11100

2. 15651/4838

3. 11100/2419

4. 1897/3162

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Correct Answer – Option 2 : 15651/4838

Given:N = 0.738738738…

M = 0.531531531…

Concept:Non-terminating repeating decimal or recurring decimal:-

A decimal fraction in which a figure or group of figures is repeated indefinitely, as in 0.7777 or as in 1.445445445.

Ex- 0.333… = 0.3̅ = 3/9

Calculation:N = 0.738738738… = \(0.\overline {738} = \frac{{738}}{{999}}\)

M = 0.531531531… = \(0.\overline {531} = \frac{{531}}{{999}}\)

⇒ N = 738/999 = 82/111

⇒ M = 531/999 = 59/111

Now,

(1/N) + (1/M) = (111/82) + (111/59)

\( ⇒ \frac{{111\: ×\: 59\:+ \:111\: × \:82}}{{82\; ×\: 59}}\)

\(⇒ \frac{{111\left( {59\; + \;82} \right)}}{{82\; ×\: 59}} = \;\frac{{111\; × \;141}}{{82\; × \:59}}\)

⇒ 15651/4838

Shortcut:Given:

N = 0.738738738…

M = 0.531531531…

Calculation:

N = 0.738738738… = \(0.\overline {738} = \frac{{738}}{{999}}\)

M = 0.531531531… = \(0.\overline {531} = \frac{{531}}{{999}}\)

⇒ N = 738/999 = 82/111

⇒ M = 531/999 = 59/111

(1/N) + (1/M) = (111/82) + (111/59)

unit digit of dominator = 2 and 9 = 2 × 9 = 18

∴ we check option which unit digit of dominator is 8, that is my answer. Inoption only option b which unit digit is 8 so that is my answer.