Raj, Mayank and Neer can complete a work in 30, 35 and 28 days, respectively.
Consider the following statements:
(A) Raj and Mayank together will complete the work in \(\displaystyle\frac{210}{13}\) days.
(B) Mayank and Neer together will complete the work in \(\displaystyle\frac{140}{3}\) days.
(C) Raj and Neer together will complete the work in \(\displaystyle\frac{420}{29}\) days.
(D) Raj, Neer and Mayank together will complete the work in \(\displaystyle\frac{420}{41}\) days.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (D) only
A person who finishes a work in \(n\) days does \(\frac{1}{n}\) of it in a day. Working together, the one-day shares are added, and the time taken is the reciprocal of the total. With the LCM of 30, 35 and 28, which is 420, the one-day shares are:
Raj \(\frac{1}{30}=\frac{14}{420}\), Mayank \(\frac{1}{35}=\frac{12}{420}\), Neer \(\frac{1}{28}=\frac{15}{420}\)
(A) Raj and Mayank together will complete the work in \(\frac{210}{13}\) days. Correct.
One day’s work: \(\frac{14+12}{420}=\frac{13}{210}\)
Time taken together: \(\frac{210}{13}\) days
(B) Mayank and Neer together will complete the work in \(\frac{140}{3}\) days. Incorrect.
One day’s work: \(\frac{12+15}{420}=\frac{9}{140}\)
Time taken together: \(\frac{140}{9}\) days, not \(\frac{140}{3}\)
(C) Raj and Neer together will complete the work in \(\frac{420}{29}\) days. Correct.
One day’s work: \(\frac{14+15}{420}=\frac{29}{420}\)
Time taken together: \(\frac{420}{29}\) days
(D) Raj, Neer and Mayank together will complete the work in \(\frac{420}{41}\) days. Correct.
One day’s work: \(\frac{14+15+12}{420}=\frac{41}{420}\)
Time taken together: \(\frac{420}{41}\) days