The ratio of boys to girls in a school is 7:5. If 20 more girls join the school, the new ratio of boys to girls becomes 7:6. What is the total number of students in the school initially?

Correct — B. Only the girls change, so write both groups with one multiplier x.

Before: boys : girls = 7x : 5x
After 20 girls join: 7x ÷ (5x + 20) = 7 ÷ 6
Cross-multiply: 42x = 35x + 140
Solve: 7x = 140 → x = 20

Initial total = 7x + 5x = 12 × 20 = 240 → option (b)

Why the others are wrong

• (a)
  200 — 200 ÷ 12 is not a whole number, so 200 students cannot split in the ratio 7 : 5 at all.
• (c)
  300 — 300 gives 175 boys and 125 girls. Adding 20 girls makes 175 : 145 = 35 : 29, not 7 : 6.
• (d)
  360 — 360 gives 210 boys and 150 girls. Adding 20 girls makes 210 : 170 = 21 : 17, not 7 : 6.

When one group changes and the other does not, the unchanged group anchors the ratio. Boys stay at 7 parts in both ratios, so the girls' move from 5 parts to 6 parts is exactly the 20 who joined.

One part = 20 students, and the school starts with 7 + 5 = 12 parts = 240.

If the unchanged group's term differed between the two ratios, you would first scale both ratios so that term matches.

Key facts

• A ratio a : b means the quantities are ax and bx for one common multiplier x.
• A total in the ratio 7 : 5 must be a multiple of 12.
• Here x = 20: 140 boys and 100 girls at first, 140 boys and 120 girls after.

Common traps

• Answering the new total, 240 + 20 = 260, when the question asks for the total initially.
• Stopping at divisibility: 240, 300 and 360 all divide by 12, so only the second ratio, 7 : 6, picks out 240.

No directly related past PYQ was found.