A father and son together can complete a piece of work in 24 days. If the father works alone for the last 6 days, then the work ends in 26 days. In how many days can the son alone complete the work?

Correct option is A

Given:
Father and son together complete the work in 24 days.
Father works alone for the last 6 days, and the total work is completed in 26 days.

Concept Used:

The rate of work of each person is the reciprocal of the time they take to complete the work. example,
A complete work in x day,
Rate of work in one day = $$\frac{1}{x}$$​ day

Solution:

Let:
Father's work rate = F (work per day)
Son's work rate = S (work per day)

(Father + Son) together complete work in 24 days

(F + S) $$\times$$​24 = 1 (total work = 1 whole unit)

​$$F + S = \frac{1}{24}$$

Father works alone for the last 6 days, and the total time taken is 26 day

(Father + Son) worked for 20 days, then Father alone worked for 6 days.

(F + S) $$\times 20$$​ + F $$\times$$​ 6 = 1

Put $$F + S = \frac{1}{24};$$

​​$$\left(\frac{1}{24} \times 20\right) + (F \times 6) = 1$$

$$\frac{20}{24} + 6F = 1$$

$$\frac{5}{6} + 6F = 1$$

$$6F = 1 - \frac{5}{6} = \frac{6-5}{6}= \frac{1}{6}$$

$$F = \frac{1}{6\times 6} = \frac{1}{36}$$

Son’s Work Rate:

​​​​​​$$S = (F + S) - F = \frac{1}{24} - \frac{1}{36} = \frac{3-2}{72}= \frac{1}{72}$$

So, son alone can complete the work in 72 days.

Thus, the correct answer is (a).