A ribbon is cut into three pieces in the ratio 2:3:5. If the length of the longest piece is 20 cm, what is the total length of the ribbon?

Correct — B.
Ratio 2 : 3 : 5 has 2 + 3 + 5 = 10 parts
The longest piece is the 5-part share = 20 cm
One part: 20 ÷ 5 = 4 cm

Pieces: 2 × 4, 3 × 4, 5 × 4 = 8, 12, 20 cm
Total: 8 + 12 + 20 = 40 cm → option (b)

Why the others are wrong

• (a)
  30 cm — 30 cm split 2 : 3 : 5 gives pieces of 6, 9 and 15 cm. Its longest piece is 15 cm, not the 20 cm the question fixes.
• (c)
  50 cm — 50 cm split 2 : 3 : 5 gives 10, 15 and 25 cm. The longest piece would be 25 cm, 5 cm more than the question allows.
• (d)
  60 cm — 60 cm split 2 : 3 : 5 gives 12, 18 and 30 cm, so its longest piece is 30 cm. A 20 cm longest piece needs a total of exactly 40 cm.

A ratio fixes the shares, not the sizes. 2 : 3 : 5 means the ribbon is cut into 10 equal parts, grouped as 2, 3 and 5.

Whichever piece the question gives you, divide its length by its own term to get one part. Then multiply by the number of parts you want — here all 10.

The longest piece carries the largest term, 5, so 20 ÷ 5 is the step that unlocks the rest.

Key facts

• A share = (its term ÷ sum of the terms) × total
• In 2 : 3 : 5 the terms sum to 10, so the shares are 20%, 30% and 50%
• Known piece ÷ its own term = the value of one part

Common traps

• Reading 20 cm as the whole ribbon and splitting it 4, 6 and 10 cm — 20 cm is the longest piece, not the total
• Dividing 20 by 10, the sum of the terms, instead of by 5, the longest piece's own term

No directly related past PYQ was found.