LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
in Commercial Mathematics by (31.5k points)
closed by

A can do a piece of work in 25 days. While B alone can do in 20 days. A started the work and was Joined by B after 10 days. The work lasted for

A. \(12\frac{1}{2}\) days

B. 15 days

C. \(6\frac{1}{2}\)

D. 25 hours

1 Answer

+1 vote
by (31.0k points)
selected by
Best answer

Number of hours A required do a piece of work : 25 

Number of hours B required do a piece of work : 20

Work done by A in one hour: \(\frac{1}{25}\)

Work done by B in one hour: \(\frac{1}{20}\)

A works alone for 10 hours, so work completed by A in 10 hours : \(10\times\frac{1}{25}=\frac{2}{5}\)

Work left = \(1-\frac{2}{5}=\frac{3}{5}\)

Work done by A and B together in one hour: \(\frac{1}{25}+\frac{1}{20}=\frac{9}{100}\)

They can do the work together in \(\frac{100}{9}\) hours.

But \(\frac{3}{5}\)th of the work is done by both A and B

∴ Time required to complete \(\frac{3}{5}\)th of the work together by A and B : \(\frac{3}{5}\times\frac{100}{9}=\frac{20}{3}\)hours

∴ Time taken to finish the work: \(\frac{20}{3}=\frac{2}{3}\)hours

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.