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:
Answer & explanation
Correct answer: option 1
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.