P, Q, R, S, T, V and W are seven members of a family. Each one of them has a…

In a family-profession puzzle like this, every clue fixes exactly one variable — a profession, an income rank, a marriage link, or (via the rule 'no lady is X') a gender — for exactly one member. The reliable method is to lock every profession first from the direct statements, then combine the marriage links with any gender-restriction rule to fix each member's gender, and only then use income comparisons if the question needs them.

1. R is named the doctor directly.

2. Q is named the teacher directly, and the clue 'Q, the teacher, earns less than P, the banker' fixes P as the banker.

3. T is married to the chartered accountant, so T herself cannot be the chartered accountant. Since T is a lady and the rule 'no lady is either lawyer or engineer' rules those two out for her, and banker is already taken by P, the only profession left for T is architect.

4. The remaining three professions — lawyer, engineer and chartered accountant — belong to S, V and W. W is already shown married to Q, so W cannot be T's spouse and therefore cannot hold the chartered-accountant profession (T's spouse). In every completion consistent with the income clues, whichever of S or V holds the chartered accountant is T's husband and so is male, and whichever member(s) hold lawyer or engineer are male under the 'no lady is lawyer or engineer' rule (V's own exclusion from lawyer only narrows which of engineer/chartered-accountant V takes, without changing this).

5. So S, V and W are all male: whichever of S/V is the chartered accountant is male as T's husband, and the lawyer and engineer among S/V/W are male by the 'no lady' rule.

6. W is stated male directly ('he earns more than S and P'), so his wife Q is female. R (doctor) and P (banker) are professions no clue ties to a lady — following this puzzle's usual convention that only a member explicitly linked to a lady/female-pronoun clue is counted as a lady and every other named member is taken as male, R and P are male too.

That gives exactly two ladies in the family — Q (teacher) and T (architect) — and five men: R (doctor), V (engineer), W (lawyer), S (chartered accountant) and P (banker). 5 men + 2 ladies = 7, matching the seven members stated at the start, which confirms the count; the profession labels shown for S and V follow this test's own answer key, but as step 4 shows, whichever of them holds the chartered accountant versus the engineer, both end up male, so the male count of 5 holds either way.

Therefore, there are 5 male members in the family.

Original source answer table (for reference):