Question

Q.9 A, B and C together can complete a work in 8 days and A alone can complete the same work in 24 days. If A and B started the work and after 2 days C also joined them, then remaining work was completed by A, B and C together in 6 days. Find in how many days B alone can complete the whole work?
A 1 28 days
B 2.36 days
C 3.24 days
D 4.32 days
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Answer 1

The number of days B alone can complete the whole work is, (none of the options match)

• Formulate an equation using the sentence that says, A, B, and C together can complete a work in 8 days and work done by A alone in 24 days.

       $A+B+C=8\\A=24$

• The LCM of 8 and 24 is 24. So the total work is 24 units.The work done by A, B, C together in one day is,

       $A+B+C=\frac{24}{8}\\ =3 {\rm unit}$

• The work done by A in one day is,

        $A=\frac{24}{24} \\=1 {\rm unit}$

• According to the given information, A and B together work for 2 days and after that C also joined them. A, B, and C work for 6 days. A, B, and C wouldn't work together from the beginning. So, find the number of days they didn't work.

         $8-6=2\, {\rm days}$

• For 2 days A and B worked. So, the work that hasn't been done by A, B, and C, in the beginning, is equal to the work done by A and B at that time.

         $(A+B+C)2=(A+B)2\\3\times 2=(1+B)2\\3=(1+B)\\B=2\, {\rm units}$

• Total work is 24 units. This work done by B alone in,

        $\frac{24}{2} =12\, {\rm days}$