Ram, Shyam and Hari can complete a work in 20, 25 and 30 days, respectively.

Consider the following statements:

(A) Ram and Shyam together will complete the work in $11\frac{1}{9}$ days.

(B) Shyam and Hari together will complete the work in 14 days.

Choose the correct answer from the options given below:

Ram completes work in 20 days, so Ram's 1 day work $= \dfrac{1}{20}$

Shyam completes work in 25 days, so Shyam's 1 day work $= \dfrac{1}{25}$

Hari completes work in 30 days, so Hari's 1 day work $= \dfrac{1}{30}$

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For Statement (A): Ram and Shyam together

Combined work $= \dfrac{1}{20} + \dfrac{1}{25}$

LCM of 20 and 25 is 100

$\dfrac{1}{20} = \dfrac{5}{100}$

$\dfrac{1}{25} = \dfrac{4}{100}$

Combined work $= \dfrac{5}{100} + \dfrac{4}{100}$

$= \dfrac{9}{100}$

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Days needed $= 1 \div \dfrac{9}{100}$

$= \dfrac{100}{9}$

$= 11\dfrac{1}{9}$ days

Statement (A) is correct.

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For Statement (B): Shyam and Hari together

Combined work $= \dfrac{1}{25} + \dfrac{1}{30}$

LCM of 25 and 30 is 150

$\dfrac{1}{25} = \dfrac{6}{150}$

$\dfrac{1}{30} = \dfrac{5}{150}$

Combined work $= \dfrac{6}{150} + \dfrac{5}{150}$

$= \dfrac{11}{150}$

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Days needed $= 1 \div \dfrac{11}{150}$

$= \dfrac{150}{11}$

$= 13\dfrac{7}{11}$ days

This is not equal to 14 days.

Statement (B) is incorrect.

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Only statement (A) is correct.