If ‘P’ denotes ‘addition’, ‘D’ denotes ‘subtraction’, ‘S’ denotes ‘multiplication’, and ‘V’ denotes ‘division’, then what will be the value of the following expression? {20 D (25 D 33)} V {− 5 S 4 D (− 6)} P 56 V (− 27 P 13)

Correct — A.
Rule: replace P, D, S, V with +, −, ×, ÷, then solve the brackets first.
{20 − (25 − 33)} ÷ {−5 × 4 − (−6)} + 56 ÷ (−27 + 13)

First bracket: 25 − 33 = −8, so 20 − (−8) = 28
Second bracket: −5 × 4 = −20, so −20 − (−6) = −14
Third bracket: −27 + 13 = −14

Divide: 28 ÷ (−14) = −2 and 56 ÷ (−14) = −4
Add: −2 + (−4) = −6 → option (a).

Why the others are wrong

• (b)
  6 — 6 has the right size and the wrong sign. Both terms are negative, −2 and −4, so their sum is −6.
• (c)
  4 — 4 is the size of 56 ÷ (−14) with its sign lost. That term is −4, and the first part, −2, still has to be added to it.
• (d)
  −4 — −4 is only the last term, 56 ÷ (−14). The first part, 28 ÷ (−14) = −2, is added to it: −2 + (−4) = −6.

Letter-coded operations work like sign substitution: rewrite the expression with real signs, then follow BODMAS. Brackets come first, then division and multiplication, then addition and subtraction.

The traps here are the negative numbers. Subtracting a negative adds: 20 − (−8) = 28, and −20 − (−6) = −14. A positive divided by a negative is negative: 28 ÷ (−14) = −2.

Key facts

• Subtracting a negative number adds it: a − (−b) = a + b.
• A positive number divided by a negative one is negative: 56 ÷ (−14) = −4.
• In this item P = +, D = −, S = × and V = ÷.

Common traps

• Working 20 − (−8) as 12 instead of 28
• Stopping at the last term, 56 ÷ (−14), and choosing −4

No directly related past PYQ was found.