Simplify: [25 − 48 ÷ 6 + 12 × 2] + 78 − [5 + 3 of (25 − 2 × 10)]

Correct — D. Reduce each bracket to a single number first, then read what is left from left to right.

First bracket: 48 ÷ 6 = 8 and 12 × 2 = 24
25 − 8 + 24 = 41

Second bracket: 25 − 2 × 10 = 25 − 20 = 5
3 of 5 = 15, so 5 + 15 = 20

41 + 78 − 20 = 99 → option (d)

Why the others are wrong

• (a)
  89 — 89 needs the second bracket to come to 30. Inside it the multiplication goes first, so 25 − 2 × 10 = 5 and 5 + 3 of 5 = 20, leaving no way to reach 30.
• (b)
  90 — 90 needs the second bracket to be 29. The inner bracket is 5 and 3 of 5 is 15, so the only value available is 5 + 15 = 20.
• (c)
  98 — 98 needs the first bracket to be 40. But 48 ÷ 6 = 8 and 12 × 2 = 24, so 25 − 8 + 24 = 41 exactly, with no slack anywhere.

BODMAS is the whole question, and the word of is what decides it.

'Of' is a multiplication that ranks above division, so 3 of 5 = 15 and would be settled first if a division stood beside it. Nothing divides it here, so it behaves as an ordinary product.

Inside every bracket the same order applies: multiply and divide before adding and subtracting. That turns 25 − 2 × 10 into 25 − 20, not 23 × 10.

Key facts

• In BODMAS 'of' is a multiplication resolved ahead of division.
• 25 − 48 ÷ 6 + 12 × 2 = 25 − 8 + 24 = 41.
• 5 + 3 of (25 − 2 × 10) = 5 + 3 of 5 = 5 + 15 = 20.
• 41 + 78 − 20 = 99.

Common traps

• Adding 8 + 24 before subtracting from 25, which turns the first bracket into −7
• Reading 25 − 2 × 10 as (25 − 2) × 10 = 230
• Treating 'of' as an ordinary multiplication when a division sits beside it

No directly related past PYQ was found.