48 Views

Question : Pawan can do a piece of work in 32 days. He worked for 8 days and left the work. Thereafter Sandeep finished the remaining work in 27 days. In how many days can Pawan and Sandeep together do the whole work?

Option 1: $16 \frac{16}{17}$ days

Option 2: $16 \frac{13}{17}$ days

Option 3: $16 \frac{15}{17}$ days

Option 4: $16 \frac{14}{17}$ days


Team Careers360 14th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

Correct Answer: $16 \frac{16}{17}$ days


Solution : Let the total work be represented by $W$.
Pawan can complete the work in 32 days, so his daily work rate is $\frac{W}{32}$.
Pawan worked for 8 days, so the work done by Pawan in 8 days is $8\times\frac{W}{32}=\frac{W}{4}​$.
The remaining work to be done is $W-\frac{W}{4} = \frac{3W}{4}$
Now, Sandeep will finish the remaining work in 27 days.
Sandeep's daily work rate is $\frac{\frac{3W}{4}}{27}=\frac{3W}{108}=\frac{W}{36}$​
Now, let $x$ be the number of days Pawan and Sandeep together can do the whole work.
The work done by Pawan in $x$ days is $x\times\frac{W}{32}$
The work done by Sandeep in $x$ days is $x\times\frac{W}{36}​$
The sum of their work must equal the total work:
⇒ $\frac{W}{32}x​+\frac{W}{36}​x=W$
⇒ $\frac{9W}{288}x + \frac{8W}{288}x = W$
⇒ $\frac{17W}{288}x = W$
⇒ $x = \frac{288}{17} = 16\frac{16}{17}$
Hence, the correct answer is $16\frac{16}{17}$ days.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books