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
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the one-day work of people working together is added; the time taken together is 1 divided by that sum.
(A) Ram and Shyam together will complete the work in \(11\frac{1}{9}\) days. Correct.
One day’s work of Ram and Shyam together: \(\displaystyle \frac{1}{20}+\frac{1}{25}=\frac{5+4}{100}=\frac{9}{100}\)
Time together \(\displaystyle =\frac{100}{9}=11\frac{1}{9}\) days
(B) Shyam and Hari together will complete the work in 14 days. Incorrect.
They take \(13\frac{7}{11}\) days, not 14:
One day’s work of Shyam and Hari together: \(\displaystyle \frac{1}{25}+\frac{1}{30}=\frac{6+5}{150}=\frac{11}{150}\)
Time together \(\displaystyle =\frac{150}{11}=13\frac{7}{11}\) days