Question

two persons of different efficiencies can do a work in 32 minutes if they work together. If the first person work for 6 minutes and second person work for 12 minutes they would left with (3/4th ) of the entire work. How many minutes would less efficient person would take to complete the work.​

Answer 1

Let the Work to be done be : W

Let the Two Persons be : P and Q

Given : P and Q can do the Work in 32 Minutes if they work together

Work done be P and Q together in One Minute :

$\mathsf{\implies P + Q = \dfrac{W}{32}}$

$\mathsf{\implies P = \dfrac{W}{32} - Q}$

$\textsf{Given : If P work's for 6 Minutes and Q work's for 12 Minutes they }\\\\\mathsf{would\;left\;with\;\bigg(\dfrac{3}{4}\bigg)^{th}\;of\;the\;entire\;work}$

$\bigstar\;\;\textsf{If P work's for 6 Minutes and Q work's for 12 Minutes they }\\\\\mathsf{would\;do\;a\;work\;of : \bigg(W -\dfrac{3W}{4}\bigg) = \bigg(\dfrac{4W - 3W}{4}\bigg) = \bigg(\dfrac{W}{4}\bigg)}$

$\mathsf{\implies 6P + 12Q = \dfrac{W}{4}}$

$\mathsf{\implies 6(P + 2Q) = \dfrac{W}{4}}$

$\mathsf{\implies P + 2Q = \dfrac{W}{24}}$

Substituting the value of P in the above equation, We get :

$\mathsf{\implies \dfrac{W}{32} - Q + 2Q = \dfrac{W}{24}}$

$\mathsf{\implies Q = \bigg(\dfrac{W}{24} - \dfrac{W}{32}\bigg)}$

$\mathsf{\implies Q = \bigg(\dfrac{4W - 3W}{96}\bigg)}$

$\mathsf{\implies Q = \dfrac{W}{96}}$

$\mathsf{It\;means : Q\;do's\;a\;work\;of\;\dfrac{W}{96}\;in\;One\;Minute}$

$\implies \textsf{Q completes the Entire Work in 96 Minutes}$

$\mathsf{Substituting\;the\;value\;of\;Q\;in\;\bigg(P = \dfrac{W}{32} - Q\bigg),\;We\;get :}$

$\mathsf{\implies P = \bigg(\dfrac{W}{32} - \dfrac{W}{96}\bigg)}$

$\mathsf{\implies P = \bigg(\dfrac{3W - W}{96}\bigg)}$

$\mathsf{\implies P = \bigg(\dfrac{2W}{96}\bigg)}$

$\mathsf{\implies P = \dfrac{W}{48}}$

$\mathsf{It\;means : P\;do's\;a\;work\;of\;\dfrac{W}{48}\;in\;One\;Minute}$

$\implies \textsf{P completes the Entire Work in 48 Minutes}$

As, P completes the Entire Work in 48 Minutes and Q completes the Entire Work in 96 Minutes, We can Notice that : P is More Efficient in completing the Work than Q

So, We can conclude that : Q is the Less Efficient Person

The Question is : How many minutes would less efficient person would take to complete the work ?

Answers :

★  Q is the Less Efficient Person

★  Q takes 96 Minutes to complete the Entire Work

Answer 2

this is the best explanation brother

I know you are preparing for competitive examinations

see atttlachment