If ‘P’ denotes ‘addition’, ‘D’ denotes ‘subtraction’, ‘S’ denotes ‘multiplication’, and ‘V’ denotes ‘division’, then what will be the value of the following expression? (48 V 8 P 25 D 6 S 4 P 3) D (25 V 5 S 3 D 4 S 3)

Correct — D.
Rule: replace the letters, then apply BODMAS inside each bracket.

First bracket: 48 ÷ 8 + 25 − 6 × 4 + 3
÷ and × first: 6 + 25 − 24 + 3
Then left to right: 10

Second bracket: 25 ÷ 5 × 3 − 4 × 3
÷ and × left to right: 5 × 3 = 15, and 4 × 3 = 12
Subtract: 15 − 12 = 3

Outer D is minus: 10 − 3 = 7 → option (d).

Why the others are wrong

• (a)
  4 — 4 is what you get if the final + 3 in the first bracket is dropped: 6 + 25 − 24 = 7, and 7 − 3 = 4.
• (b)
  5 — 5 would need the first bracket to be 8. It is 6 + 25 − 24 + 3 = 10.
• (c)
  6 — 6 would need the second bracket to be 4. It is 25 ÷ 5 × 3 − 4 × 3 = 15 − 12 = 3.

Letter-for-operation items test two things in order: substitution, then BODMAS. Rewrite the whole expression in ordinary signs before calculating anything, because working straight from the letters invites a swapped sign.

Inside each bracket, do ÷ and × first, left to right, then + and −, left to right. Then subtract the second bracket from the first.

Key facts

• BODMAS: brackets, then division and multiplication left to right, then addition and subtraction left to right.
• Here P = +, D = −, S = × and V = ÷.
• The first bracket is 10 and the second is 3.

Common traps

• Missing the D between the brackets and adding 10 and 3
• Working the second bracket strictly left to right, so 15 − 4 = 11 and then 11 × 3

No directly related past PYQ was found.