Ajay, Bablu and Chirag can complete a certain work in 21, 28 and 15 days respectively. Ajay and Chirag started the work while Bablu joined them after 5 days and worked with them till the completion of the work. For how many days Bablu worked ?

Correct option is B

Given:

Ajay can do the work in 21 days.

Bablu can do the work in 28 days.

Chirag can do the work in 15 days.

Ajay and Chirag work for the first 5 days; then Bablu joins till completion.

Solution:

Let x be Bablu’s working days after day 5.
Rates: A$$=\frac1{21};B=\frac1{28};C=\frac1{15}$$​​
Work equation:
5(A+C)+x(A+B+C)=1.
A+C=$$\frac{1}{21}+\frac{1}{15}=\frac{12}{105}=\frac{4}{35},$$​

A+B+C$$=\frac{1}{21}+\frac{1}{28}+\frac{1}{15}=\frac{3}{20}.$$​​
So

​$$5\times\frac{4}{35}+x\times\frac{3}{20}=1 \\ \ \\\frac{20}{35}+x\cdot\frac{3}{20}=1\\ \ \\\frac{4}{7}+x\cdot\frac{3}{20}=1 \\ \ \\x\cdot\frac{3}{20}=1-\frac{4}{7}=\frac{3}{7}\\ \ \\x=\frac{3}{7}\times\frac{20}{3}=\frac{20}{7}\text{ days}.$$​​

So, Bablu worked $$2\frac{6}{7}$$​​ days.

Alternate Method:

Work–rate method with total work = LCM(21,28,15)=420 units.

Daily rates: A$$=\frac{420}{21}=20, B=\frac{420}{28}=15, C=\frac{420}{15}=28$$​units/day.

First 5 days by Ajay & Chirag: rate = 20 + 28 = 48 units/day.
Work done =$$5\times48=240$$​units.

Remaining work = 420 - 240 = 180 units.

With all three: rate = 20 + 15 + 28 = 63 units/day.
Time to finish =$$\dfrac{180}{63}=\dfrac{20}{7}$$​days $$=2\frac{6}{7}$$​days.

So, Bablu worked $$2\frac{6}{7}$$​ days.