Question

A and b together can complete the work in 36 days, b and c together can complete the work in 40 days. If a worked for 15 days and b worked for 20 days, then the remaining work is done by c alone in 38 days. In how many days a alone can complete the work?

Answer 1

Answer:

it is difficult

Step-by-step explanation:

Answer 2

THE a CAN COMPLETE THE WORK ALONE IN 60 DAYS

Step-by-step explanation:

Let 'a' can finish the piece of work in x days

Let 'b' can finish the piece of work in y days

Let 'c' can finish the piece of work in z days

∴ a's one day's work is = $\frac{1}{X}$

  b's one day's work is $=\frac{1}{Y}$

  c's one day's work is $=\frac{1}{Z}$

A/Q

        $\frac{1}{X} +\frac{1}{Y} =\frac{1}{36}$ ...... EQ (1)

       $\frac{1}{Y} +\frac{1}{Z} =\frac{1}{40}$  .......EQ(2)

a's 15 day's work = $\frac{15}{X}$

b's 20 day's work =$\frac{20}{Y}$

Remaining work is = $1-\frac{15}{X} -\frac{20}{Y}$

                             = $1-\frac{15}{X} -20( \frac{1}{36} -\frac{1}{X} )$

                            =$1-\frac{15}{X}-\frac{20}{36} +\frac{20}{X}\\\\\frac{16}{36} +\frac{5}{X}$

 The remaining work is done by c in 38 days

∴  

      38 = remaining work / work done by c in one day

      $\frac{\frac{4}{9}+\frac{5}{X} }{\frac{1}{Z} } =38\\\frac{4}{9}=\frac{38}{Z}-\frac{5}{X}$........EQ(3)

Subtracting EQ(2) from equation EQ(1) we get

      $\frac{1}{X} -\frac{1}{Z} =\frac{1}{360}$......EQ(4)

NOW , 5 EQ(4) + EQ(3) we get

    $\frac{5}{X}-\frac{5}{Z} +\frac{38}{Z} -\frac{5}{X}=\frac{1}{360} +\frac{4}{9}$

              $\frac{33}{Z} =\frac{11}{24}$

           $Z=72$

∴ The work done by c alone is 72

Now the put value of Z in EQ(4) we get

             $\frac{1}{X} -\frac{1}{72} =\frac{1}{360}$

              $\frac{1}{X}=\frac{1}{360} +\frac{1}{72}$

             $\frac{1}{X} =\frac{1}{60}$

            $X=60$

HENCE THE a CAN FINISH THE WORK ALONE IN 60 DAYS .