We know that, formula for average,

$(\Rightarrow \left\{ {{A_E} = \frac{{{S_E}}}{{{n_E}}}\;or\;{S_E} = {A_E} \times {n_E}} \right\})$

where,

S_E = SUM of ENTITIES,

n_E = number of entities,

A_E = Average of entities.

Now, according to the question,

Average salary of 5 members of the group earlier = Rs 25000

∴ Total salary of 5 members of the group earlier = 25000 × 5 = Rs 125,000

Now, when one old member is replaced by a new member whose salary is Rs 22,000, the average salary of the group decreases by Rs 1000,

Average salary of 5 members of the group later = Rs (25000 – 1000) = Rs 24000

∴ Total salary of 5 members of the group later = Rs 24000 × 5 = Rs 120,000

Hence, salary of the outgoing member = (total salary of the group earlier – total salary of the group later) + salary of the incoming member

⇒ Salary of the replaced (outgoing) member = Rs (125,000 – 120,000) + Rs 22,000

= Rs (22,000 + 5000) = Rs 27,000

Hence, the REQUIRED salary of the outgoing member is Rs 27,000.

Alternatively:

The average salary decrease by 1000, so sum of salary decreases by 5 × 1000 = Rs. 5000, hence salary of new member is 5000 less than the salary of the replaced member.

∴ Salary of replaced (outgoing) member = Rs (22000 + 5000) = Rs 27000.

Alternatively:

Let the salary of the replaced (outgoing) member be Rs ‘x’, then according to the question,

$(\frac{{\left( {25000 \times 5} \right) + 22000 - x}}{5} = 24000)$

⇒ 22000 – x = 5 (24000 – 25000)

⇒ 22000 - x = - 5000

⇒ x = 22000 + 5000 = 27000