The ratio between male and female members in a club is 2 : 3. If the number of male members is increased by 200, the ratio becomes 5 : 6. How many female members are there in the club?

Correct — C. Write the members as 2x male and 3x female, which holds the 2 : 3 ratio while leaving one unknown to solve for.

After 200 men join: (2x + 200) : 3x = 5 : 6
Cross-multiply: 6(2x + 200) = 15x
Expand: 12x + 1200 = 15x, so 3x = 1200 and x = 400
Female members = 3x = 1200 → option (c)

Check: 800 + 200 = 1000 against 1200 is 5 : 6.

Why the others are wrong

• (a)
  1400 — 1400 women would force 2⁄3 × 1400 = 933.33 men, not a whole number of people, so it cannot sit in a 2 : 3 ratio at all.
• (b)
  1000 — 1000 is the male count after the 200 join (800 + 200) — a number you pass through on the way to the answer, not the female count asked for.
• (d)
  900 — Take 900 women and the men are 600, so after the increase the ratio is 800 : 900 = 8 : 9, not 5 : 6.

A ratio is not a count. Writing the groups as 2x and 3x fixes their proportion while leaving a single unknown, and that substitution is the whole item.

The change acts on one group only, so 3x carries through untouched into the second proportion. Cross-multiplying turns that proportion into a linear equation, and the multiplier x is recovered before any real count is read off.

Key facts

• A 2 : 3 ratio means the counts are 2x and 3x for some positive multiplier x.
• Here x = 400, so the club starts with 800 male and 1200 female members.
• After 200 men join, 1000 : 1200 reduces to 5 : 6.

Common traps

• Answering with the male count after the increase instead of the female count.
• Adding 200 to the ratio term and writing (2 + 200) : 3.
• Assuming the female side changes too, when the stem moves only the men.

No directly related past PYQ was found.