Question

A can do a work in 6 hours B can do it 5 hours. A,B and C together can do a work in 2 hours are required find out how many hours are required to complete the work by C?​

Answer 1

Question:

• A can do a work in 6 hours B can do it 5 hours. A,B and C together can do a work in 2 hours are required find out how many hours are required to complete the work by C ?​

Answer:

• The time taken by C to complete the work is 7 ¹/₂ hours

Explanation:

Given that :

• A can do a work in 6 hours B can do it 5 hours
• A,B and C together can do a work in 2 hours

To Find:

• How many hours will C require to complete the work alone

Required Solution:

• As per the given information

★ We can state that ,

${ \pink {\bigstar \; \; {\boxed{\bf{ A + B + C _{(Time \; taken \; by \; A,B , C)}= 2 hours }}}}}$  

★ The work done by them in 1 hour will be ,

${ \pink {\bigstar \; \; {\boxed{\bf{ \dfrac{1}{A + B + C} _{(Work \; done \; by \; A,B , C \; 1 \; hour)}= \frac{1}{2} }}}}}$  

★ As per first statement ,

${ \purple {\bigstar \; \; {\boxed{\bf{ A _{(Time \; taken \; by \; A)}= 6hours }}}}}$  

★ Work done by A in 1 hour will be ,

${ \purple {\bigstar \; \; {\boxed{\bf{ A _{(Work \; done\; by \; A \; 1 \; hour)}= \dfrac{1}{6} }}}}}$  

★ As per second statement ,

${ \blue {\bigstar \; \; {\boxed{\bf{ B _{(Time \; taken \; by \; B)}=5hours }}}}}$

★ Work done by B in 1 hour will be ,

${ \blue {\bigstar \; \; {\boxed{\bf{ B _{(Work \; done\; by \; B\; 1 \; hour)}= \dfrac{1}{5} }}}}}$  

According to the question:

• We have been given the time taken by A and B to do the work and the time taken by A, B , C to do the total work , so now as we have found the 1 hour work of A , B and the 1 hour work of A , B , C if they work togeather so , let's find the time taken by c with the help of the 1 hour work of A and B

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★ we can state that ,

$\longrightarrow \footnotesize \sf \dfrac{1}{A + B + C} = \dfrac{1}{2}$

$\longrightarrow \footnotesize \sf \dfrac{1}{A} + \dfrac{1}{B} + \dfrac{1}{C} = \dfrac{1}{2}$

$\longrightarrow \footnotesize \sf \dfrac{1}{6} + \dfrac{1}{5} + \dfrac{1}{C} = \dfrac{1}{2}$

$\longrightarrow \footnotesize \sf \dfrac{5}{30} + \dfrac{6}{30} + \dfrac{1}{C} = \dfrac{1}{2}$

$\longrightarrow \footnotesize \sf \dfrac{1}{C} = \dfrac{1}{2} - \dfrac{11}{30}$

$\longrightarrow {\footnotesize {\sf {\red{\underline{\underline{ \dfrac{1}{C} = \dfrac{4}{30} }}}}}}$

★ Henceforth ,

${ \red {\bigstar \; \; {\boxed{\bf{C _{(Time \; taken \; by \; A)}= \frac{30}{4} hours}}}}}$  

Therefore:

• The time taken by C to complete the work is 7 ¹/₂ hours

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