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:

(A) only

The correct answer is Option (1) → (A) only

Let us check each statement using work–time concepts.

Given:

• Ram’s time = 20 days → Rate = $\frac{1}{20}$​
• Shyam’s time = 25 days → Rate = $\frac{1}{25}$​
• Hari’s time = 30 days → Rate = $\frac{1}{30}$​

Statement (A)

Ram + Shyam rate

$\frac{1}{20} + \frac{1}{25} = \frac{5 + 4}{100} = \frac{9}{100}$

Time taken

$= \frac{100}{9} = 11 \frac{1}{9}\text{ days}$

So, Statement (A) is correct.

Statement (B)

Shyam + Hari rate

$\frac{1}{25} + \frac{1}{30} = \frac{6 + 5}{150} = \frac{11}{150}$

Time taken

$= \frac{150}{11} \approx 13.64\text{ days}$

This is not equal to 14 days, so Statement (B) is incorrect.