A, B and C together finish a work in 4 days if A alone can finish the same work in 8 days and B in 12 days. Find how long will C take to finish the work?
Given:
A, B and C together finish a work in 4 days.
A alone can finish the work in 8 days and B in 12 days.
To find: Here we have to find how long will C take to finish the work.
Solution:
We would consider total work to be 1
Work done by A in one day = $\frac{Total work}{Total number of days taken}$
Work done by A in one day = $\frac{1}{A}$
Work done by A in one day = $\frac{1}{12}$
Similarly, work done by B and C is $\frac{1}{18}$ and $\frac{1}{C}$ respectively.
Therefore,
Total work done by all three in one day = $\frac{1}{12}\ +\ \frac{1}{18}\ +\ \frac{1}{C}$
Work done in one day $\times$ Total number of days = Total work
$[\frac{1}{12}\ +\ \frac{1}{18}\ +\ \frac{1}{C}]\ \times\ 4\ =\ 1$
$\frac{1}{12}\ +\ \frac{1}{18}\ +\ \frac{1}{C}\ =\ \frac{1}{4}$
$\frac{1}{C}\ =\ \frac{1}{4}\ -\ \frac{1}{12}\ -\ \frac{1}{18}$
$\frac{1}{C} \ =\ \frac{9\ -\ 3\ -\ 2}{36}$
$\frac{1}{C} \ =\ \frac{4}{36}$
$\frac{1}{C} \ =\ \frac{1}{9}$
C = 9 days
So, C can complete the same work in 9 days.
Related Articles
- A and B together can do a piece of work in 10 days if an alone will take 12 days to finish the work how long will B take to do the work?
- A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
- 2 women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery and that taken by 1 man alone.
- Anil Sunil and Rajat can complete a work in 4 hours. If Anil does the work in 12 hour, Sunil in 10 hours . How long it take to Rajat to finish the alone
- A, B and C can do a piece of work in 20,30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
- Debel completes his work in $\frac{7}{9}$ days. Arun takes $\frac{3}{2}$ times more time than Debel to finish his work. Find the number of days that Arun needs to complete his work.
- 2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?
- A, B, and C can reap a field in $15\frac{3}{4}$ days; B, C, and D in 14 days; C, D, and A in 18 days; D, A, and B in 21 days. At what time can A, B, C, and D together reap it?
- Udit can complete his work in 10 days. What amount of work will be completed in eight days?
- How to Convert Hours to 8-Hour Work Days in Excel?
- Formulate the following problems as a pair of equations, and hence find their solutions:(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately
- If john works for 5 days, he will get rupees 350. How much will he get, if he work for 20 days?
- A, B, C can do a work in 15hr, 12hr, 20hr respectively. At 4.00 pm, they started working together and after working for 2hr, a left the work and b left 2hr before completion of the work in what time the whole work will be completed.
- Find minimum speed to finish all Jobs in C++
- A labour gets Rs. 675 for nine days work. How many days should he worked to get Rs. 900?
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies