A, B and C working together take 8 min. to address a pile of envelopes. A and B together would take 10 min; A and C together would take 15 min. How long would each take working alone?
Answers
by
pratik2040
29.12.2018
Math
Secondary School
A,B,C working together take 8 Minute to address a pile of envelope A and B together would take 10 minutes and A and C together would take 15 minutes. how long would it take Walking Alone?
dipanshudhoundiyal17
dipanshudhoundiyal17
Answer:
Step-by-step explanation:
hope this helps you
sharonr
Time taken by A alone to complete work = 8 minutes
Time taken by B alone to complete work = 10 minutes
Time taken by C alone to complete work = 15 minutes
Solution:
Given:-
• A,B,C working together take 8 Minute
• A and B together would take 10 minutes
• A and C together would take 15 minutes
Find:- . How long would it take Working Alone
Let the total amount of work be the L.C.M of the work mention above in question
L.C.M(8, 10, 15) = 120
\text { Efficiency }=\frac{\text { Total Work }}{\text { Time Taken }}
\text { Efficiency of }(\mathrm{A}+\mathrm{B}+\mathrm{C})=\frac{120}{8}=15 / \mathrm{minute} ------ eqn 1
\text { Efficiency of }(A+B)=\frac{120}{10}=12 / \text { minute } ------ eqn 2
\text { Efficiency of }(\mathrm{A}+\mathrm{C})=\frac{120}{15}=8 / \mathrm{minute} ------- eqn 3
Solving Equation (1), (2) and (3) , we get
Efficiency of C = 3/minute
Efficiency of B = 7/minute
Efficiency of A = 5/minute
Now, the time taken by each to complete work is
\text { Time taken }=\frac{\text { Total Work }}{\text { Efficiency }}
\begin{array}{l}{\text { Time taken by A to complete work }=\frac{120}{15}=8 \text { minutes }} \\\\ {\text { Time taken by B to complete work }=\frac{120}{12}=10 \text { minutes }} \\\\ {\text { Time taken by C to complete work }=\frac{120}{8}=15 \text { minutes }}\end{array}